
<PAGE>
 
                                                                  EXHIBIT 10.5

                              CRITICAL PATH, INC.
                              ------------------- 

                        AMENDMENT TO SERIES B PREFERRED
                        -------------------------------
                           STOCK PURCHASE AGREEMENT
                           ------------------------


     THIS AMENDMENT TO SERIES B PREFERRED STOCK PURCHASE AGREEMENT (the
"Amendment") is made as of January 13, 1999, by and among CRITICAL PATH, INC., a
California corporation (the "Company"), and the investors listed on the Schedule
of Investors attached hereto as Exhibit A (each an "Investor," collectively the
"Investors").

                                 RECITALS

     A.  The Company and certain Investors have entered into that certain Series
B Preferred Stock Purchase Agreement dated September 11, 1998 (the "Purchase
Agreement"), pursuant to which the Company sold and certain Investors purchased
8,000,827 shares of Series B Preferred Stock of the Company.

     B.  The Purchase Agreement provides for the adoption of the Amended and
Restated Articles of Incorporation (the "Restated Articles") which allows for
the issuance of up to 13,904,558 shares of Series B Preferred Stock, and the
Company desires to sell up to an additional 8,095,442 shares of Series B
Preferred Stock (the "Additional Shares") to certain Investors on the same terms
and conditions set forth in the Purchase Agreement.

     C.  The Company proposes amending relevant sections of the Purchase
Agreement to provide for a second closing at which the Company may sell the
Additional Shares (the "Second Closing").

     NOW, THEREFORE, the parties to this Amendment hereby agree as follows
effective upon the Second Closing:

     1.  Paragraph (a) of Section 1.1 of the Purchase Agreement is hereby
amended to read in its entirety as follows:

     "(a) The Company shall adopt and file with the Secretary of State of the
State of California on or before the Closing (as defined below) the Amended and
Restated Articles of Incorporation in the form attached hereto as Exhibit B (the
"Restated Articles").  The Restated Articles authorize the Company to sell and
issue up to 13,904,558 shares of its Series B Preferred Stock, having the
rights, privileges and preferences as set forth in the Restated Articles.
Attached hereto as Exhibit B-1 is the form of Certificate of Amendment of
Articles of Incorporation increasing the authorized number of shares of Series B
Preferred Stock from 13,904,558 to 22,000,000 (the "Certificate of Amendment"),
which the Company shall, prior to the Second Closing of the sale of any
additional shares, adopt and file with the California Secretary of State."

     2.  Paragraph (a) of Section 1.2 of the Purchase Agreement is hereby
amended to read in its entirety as follows:

                                      -1-
<PAGE>
 
     "(a)  The purchase and sale of the Shares shall take place at the offices
of Pillsbury Madison & Sutro LLP, 2550 Hanover Street, Palo Alto, California, at
2:00 p.m., on September 11, 1998, or at such other time and place as the Company
and the Investors acquiring in the aggregate more than half the Shares to be
sold hereunder shall mutually agree, either orally or in writing (which time and
place are designated as the "Closing").  As used in this Agreement, the term
"Closing" shall apply to the September 11, 1998 closing (the "First Closing") or
the January __, 1999 closing (the "Second Closing"), whichever is relevant to
the Investor executing this Agreement."

     3.  Section 1.3  of the Purchase Agreement is hereby amended to read in its
entirety as follows:

     "1.3  Subsequent Sale of Series B Preferred Stock.  If less than all of the
authorized number of shares of Series B Preferred Stock are sold at the Closing,
for a period up to and through January 31, 1999 (the "Subsequent Period") the
Company may sell up to the balance of the authorized but unissued Series B
Preferred Stock to such persons as are approved by the Company's Board of
Directors and who meet the suitability requirements set forth in Section 3.6
hereof at the same price per share as the Series B Preferred Stock purchased and
sold at the Closing (each a "Subsequent Closing").  Any such sale shall be upon
the same terms and conditions as those contained herein, and such persons or
entities shall become parties to this Agreement, the Amended and Restated
Investors' Rights Agreement in the form attached as Exhibit C (the "Investors'
Rights Agreement"), the Amended and Restated Right of First Refusal and Co-Sale
Agreement in the form attached as Exhibit D (the "Co-Sale Agreement") and the
Amended and Restated Voting Agreement in the form attached as Exhibit E (the
"Voting Agreement") (collectively the "Other Agreements"), and shall have the
rights and obligations of an Investor hereunder and thereunder."

     4.  Paragraph (a) of Section 2.5 of the Purchase Agreement is hereby
amended to read in its entirety as follows:

     "(a)   51,234,743 shares of preferred stock (the "Preferred Stock"),
29,234,743 shares of which have been designated Series A Preferred Stock (the
"Series A Preferred Stock"), 27,987,803 of which are issued and outstanding
immediately prior to the Closing, and 22,000,000 shares of which have been
designated Series B Preferred Stock, none of which is issued and outstanding
immediately prior to the First Closing.  The rights, privileges and preferences
of the Series A Preferred Stock and the Series B Preferred Stock will be as
stated in the Restated Articles.  Under the terms of the Certificate of
Amendment attached hereto as Exhibit B-1, the capitalization of the Company
immediately prior to the Second Closing is as set forth above, except that
8,000,827 shares of Series B Preferred Stock shall be issued and outstanding
immediately prior to the Second Closing."

     5.  Section 6.9 of the Purchase Agreement is hereby amended to read in its
entirety as follows:

     "6.9 Expenses.  The Company and each Investor shall pay their respective
costs and expenses incurred with respect to the negotiation, execution, delivery
and performance of this Agreement; provided, however, that if the First Closing
is effected, the Company shall promptly pay the reasonable fees and expenses of
Brobeck Phleger & Harrison LLP, special counsel for

                                      -2-
<PAGE>
 
the largest Investor in the First Closing, not to exceed $15,000. In addition,
if the Second Closing is effected, the Company shall promptly pay the reasonable
fees and expenses of special counsel for the largest Investor in the Second
Closing, as set forth in Exhibit A, not to exceed $15,000."

     6.  The Purchase Agreement shall be amended to add Exhibit B-1, the form of
Certificate of Amendment of Articles.  Other exhibits to the Purchase Agreement
shall be amended as appropriate to reflect the Second Closing.

     7.   Each Investor shall have received from Pillsbury Madison & Sutro LLP,
counsel for the Company, an opinion dated as of the Second Closing.

     8.  Investors who are listed on Exhibit A under the heading "Second
Closing," by executing this Amendment, are also executing and becoming parties
to the Purchase Agreement, as amended hereby, and such investors hereby confirm
to the Company the investor representations and warranties set forth in Section
3 thereof.

     9.  Except as expressly modified herein, the Purchase Agreement shall
remain in full force and effect.

     This Amendment to Series B Preferred Stock Purchased Agreement may be
executed in any number of counterparts, each of which shall be an original, but
all of which together shall constitute one and the same instrument.



                                       COMPANY:

                                       CRITICAL PATH, INC.
                                       a California corporation


                                       By /s/  Douglas Hickey
                                          --------------------------------------
                                                    Douglas Hickey           
                                          President and Chief Executive Officer

                                      -3-
<PAGE>
 
                                       INVESTORS:

                                       E*TRADE Group, Inc.

                                       By  /s/
                                          -------------------------------------

                                       Title          CFO
                                            -----------------------------------


                                       BENCHMARK CAPITAL PARTNERS II, L.P.
                                       as nominee for
                                       Benchmark Capital Partners II, L.P.,
                                       Benchmark Founders Fund II, L.P.,
                                       Benchmark Founders Fund II-A, L.P. and
                                       Benchmark Members' Fund II, L.P.

                                       By:  Benchmark Capital Management Co. II,
                                       L.L.C., general partner

                                       By  /s/
                                          -------------------------------------
                                                    Managing Member


                                       US WEST DATA INVESTMENTS, INC.

                                       By  /s/
                                          -------------------------------------

                                       Title___________________________________


                                       HAMBRECHT & QUIST

                                       By______________________________________

                                       Title___________________________________



                     SIGNATURE PAGE TO CRITICAL PATH, INC.
              AMENDMENT TO SERIES B PREFERRED STOCK PURCHASE PLAN

                                      -4-
<PAGE>
 
                                       CMG@VENTURES II, L.L.C.

                                       By /s/
                                         --------------------------------------

                                       Title        General Partner
                                            -----------------------------------

                                       ATTRACTOR LP

                                       By /s/ Harvey Allison, MM
                                         -------------------------------------- 
 
                                       Title      Attractor Ventures LLC, GP
                                            ----------------------------------- 
                                                      Attractor LP

                                       ATTRACTOR DEARBORN PARTNERS LP
        
                                       By /s/  Harvey Allison, MM 
                                          -------------------------------------

                                       Title      Attractor Ventures LLC,GP  
                                            ----------------------------------- 
                                                      Attractor LP

                                       ATTRACTOR INSTITUTIONAL


                                       By /s/  Harvey Allison, MM
                                          -------------------------------------

                                       Title      Attractor Ventures, LLC, GP
                                            -----------------------------------
                                                       Attractor LP

                                       NETWORK SOLUTIONS, INC.

                                       By /s/ 
                                          -------------------------------------

                                       Title   Chief Financial Officer and
                                            -----------------------------------
                                               Acting Chief Operating Officer

                                       MOHR, DAVIDOW VENTURES V, L.P.


                     SIGNATURE PAGE TO CRITICAL PATH, INC.
              AMENDMENT TO SERIES B PREFERRED STOCK PURCHASE PLAN

                                      -5-
<PAGE>
 
                                       By:  Fifth MDV Partners, L.L.C.

                                       By /s/ George Zachary
                                         -------------------------------------
                                                    Managing Member

        
                                       MOHR, DAVIDOW VENTURES V, L.P., as
                                       nominee for MDV Entrepreneurs' Network
                                       Fund II(A), L.P. and MDV Entrepreneurs'
                                       Network Fund II(B), L.P.
                                       By:  Fifth MDV Partners, L.L.C.

                                       By /s/ George Zachary
                                         -------------------------------------
                                                    Managing Member


                                       THE LEVINSON FAMILY TRUST,
                                       Kathy Levinson and Jennifer Levinson,
                                       trustees, uad 1/17/94

                                       By /s/
                                         --------------------------------------
                                       Title Trustee
                                            ----------------------------------- 

                                       JERRY GRAMAGLIA

                                       /s/ Jerry Gramaglia
                                       ---------------------------------------- 

                                       THE LEONARD C. PURKIS REVOCABLE 
                                       TRUST, UAD 4/24/97

                                       By /s/
                                         --------------------------------------
                                       Title Trustee
                                            ----------------------------------- 


                     SIGNATURE PAGE TO CRITICAL PATH, INC.
              AMENDMENT TO SERIES B PREFERRED STOCK PURCHASE PLAN

                                      -6-
<PAGE>
 
                                       DEBRA J. CHRAPATY

                                       /s/ Debra J. Chrapaty
                                       ---------------------------------------- 


                                       THE COTSAKOS FAMILY TRUST

                                       By /s/
                                         --------------------------------------

                                       Title___________________________________


                                       RAMSEY/BEIRNE INVESTMENT POOL II, L.L.C.

                                       By  /s/
                                         --------------------------------------

                                       Title Member / CFO
                                            ----------------------------------- 


                     SIGNATURE PAGE TO CRITICAL PATH, INC.
              AMENDMENT TO SERIES B PREFERRED STOCK PURCHASE PLAN

                                      -7-
<PAGE>
 
                                   EXHIBIT A
                                   ---------

                             SCHEDULE OF INVESTORS
                             ---------------------

                                 First Closing
                                 -------------


                              September 11, 1998


                                     SA-1

<PAGE>
 
                             SCHEDULE OF INVESTORS
                             ---------------------

                                Second Closing
                                --------------

                               January __, 1999


                                     SA-2

<PAGE>
 
                                  EXHIBIT B-1
                                  -----------

             CERTIFICATE OF AMENDMENT OF ARTICLES OF INCORPORATION
             -----------------------------------------------------


                                     B-1-1

<PAGE>
 
                                   EXHIBIT A
                                   ---------

                            SCHEDULE OF EXCEPTIONS
                            ----------------------

                                Second Closing

                               January __, 1999


                                      D-1

