Epizyme (EPZM) 10-Q 2018 Q3 Quarterly report

Exhibit 32.1

CERTIFICATIONS OF CEO AND CFO PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with this Quarterly Report on Form 10-Q of Epizyme, Inc. (the “Company”) for the period ended September 30, 2018, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned, Robert B. Bazemore, President and Chief Executive Officer of the Company, and Suzanne Fleming, Senior Vice President, Finance and Treasurer of the Company, hereby certifies, pursuant to 18 U.S.C. (section) 1350, as adopted pursuant to (section) 906 of the Sarbanes-Oxley Act of 2002, that to the best of his knowledge:

(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.

Dated: November 2, 2018

/s/ Robert B. Bazemore

Robert B. Bazemore

President and Chief Executive Officer

(Principal Executive Officer)

/s/ Suzanne Fleming

Suzanne Fleming

Senior Vice President, Finance and Treasurer (Principal Financial Officer)