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 in the Registration Statement (Form S-1) and related Prospectus of Epizyme, Inc. dated April 18, 2013.

/s/ Ernst & Young LLP

Boston, Massachusetts

April 17, 2013