EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

This certification is not to be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, and does not constitute a part of the Quarterly Report of Seagate Technology plc (the “Company”) on Form 10-Q for the fiscal quarter ended September 27, 2013, as filed with the Securities and Exchange Commission on the date hereof (the “Report”).

In connection with the Report, we, Stephen J. Luczo, Chief Executive Officer of the Company, and Patrick J. O’Malley, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: October 29, 2013 | /s/ STEPHEN J. LUCZO
| Stephen J. Luczo
| Chairman and Chief Executive Officer
Date: October 29, 2013 | /s/ PATRICK J. O’MALLEY
| Patrick J. O’Malley
| Executive Vice President, Finance and Chief Financial Officer