Epizyme (EPZM) 10-Q 2017 Q2 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 Form10-Q of Epizyme, Inc. (the “Company”) for the period ended June 30, 2017, 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 Andrew E. Singer, Executive Vice President, Finance and Administration, Chief Financial Officer 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: August 7, 2017

/s/ Robert B. Bazemore

Robert B. Bazemore

President and Chief Executive Officer

/s/ Andrew E. Singer

Andrew E. Singer

Executive Vice President, Finance and

Administration, Chief Financial Officer and Treasurer