Exhibit 5.1

March 4, 2016

Randolph Bancorp, Inc.

10 Cabot Place

Stoughton, MA 02072

Ladies and Gentlemen:

We have acted as counsel to you in connection with the transactions contemplated by the Plan of Conversion of Randolph Bancorp approved by the Board of Trustees of Randolph Bancorp on January 26, 2016, as amended (the “Plan of Conversion”) and your filing of a Registration Statement on Form S-1 (as amended or supplemented, the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement relates to the issuance by Randolph Bancorp, Inc., a Massachusetts corporation (the “Company”) of (1) up to 5,686,750 shares of the Company’s common stock, $0.01 par value per share, to be sold in the offerings described in the Plan of Conversion (the “Offering Shares”) and (2) up to 181,976 shares of the Company’s common stock, $0.01 par value per share, to be contributed by the Company to The Randolph Savings Bank Charitable Foundation pursuant to the terms of the Plan of Conversion (the “Foundation Shares,” and together with the Offering Shares, the “Shares”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the Massachusetts Business Corporation Act (which includes reported judicial decisions interpreting the Massachusetts Business Corporation Act).

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and, upon issuance and delivery against payment therefor (with respect to the Offering Shares) or contribution (with respect to the Foundation Shares) in accordance with the terms of the Plan of Conversion, the Shares will be validly issued, fully paid and non-assessable.

Randolph Bancorp, Inc.

March 4, 2016

Page 2

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement and to the references to our firm under the caption “Legal and Tax Matters” in the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.