Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” and to the use of our report dated March 22, 2013 (except for Note 13, as to which the date is May 13, 2013) in Amendment No. 4 to the Registration Statement (Form S-1 No. 333-187982) and related Prospectus of Epizyme, Inc.

/s/ Ernst & Young LLP    

Boston, Massachusetts

May 28, 2013