Exhibit 5.1

November 2, 2016

Dominion Midstream Partners, LP

120 Tredegar Street

Richmond, Virginia 23219

Ladies and Gentlemen:

We have acted as counsel to Dominion Midstream Partners, LP, a Delaware limited partnership (the “Partnership”), in connection with (i) the offer and sale by the Partnership of 13,500,000 units representing limited partner interests in the Partnership (the “Offered Units”) pursuant to an Underwriting Agreement, dated as of October 31, 2016 (the “Underwriting Agreement”), by and among Dominion Midstream GP, LLC, a Delaware limited liability company (the “General Partner”), and the Partnership, on one hand, and RBC Capital Markets, LLC, Barclays Capital Inc. and J.P. Morgan Securities LLC, on behalf of the several underwriters named therein (the “Underwriters”), on the other hand, (ii) the sale of an additional 2,025,000 units representing limited partner interests in the Partnership (the “Option Units” and, collectively with the Offered Units, the “Units”) pursuant to the exercise by the Underwriters of an option to purchase the Option Units, and (iii) the filing of the Registration Statement on Form S-3 (Registration No. 333-207743) (the “Registration Statement”) and the prospectus included therein (the “Base Prospectus”) by the Partnership under the Securities Act of 1933, as amended (the “Act”), with the Securities and Exchange Commission (the “SEC”), pursuant to which the offering and sale of the Units are registered. The Units have been offered for sale pursuant to a prospectus supplement, dated October 31, 2016 (the “Prospectus Supplement”), filed with the SEC pursuant to Rule 424(b) promulgated under the Act, to the Base Prospectus (such Base Prospectus, as amended and supplemented by the Prospectus Supplement, the “Prospectus”). Capitalized terms used but not otherwise defined herein have the meaning ascribed to such terms in the Underwriting Agreement.

In connection with the opinion set forth below, we have examined and relied upon the following:

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In connection with rendering the opinion set forth below, we have assumed that (i) all information contained in all documents reviewed by us is true and correct; (ii) all signatures on all documents examined by us are genuine; (iii) all documents submitted to us as originals are authentic and all documents submitted to us as copies conform to the originals of those documents; (iv) the Underwriting Agreement has been duly authorized and validly executed and delivered by the Underwriters and constitutes a legal, valid and binding obligation of the Underwriters, and that the Underwriters have the requisite organizational and legal power and authority to perform their obligations under the Underwriting Agreement; (v) each certificate from governmental officials reviewed by us is accurate, complete and authentic, and all official public records are accurate and complete; and (vi) all Units will be issued and sold in the manner described in the Prospectus and the Prospectus Supplement, and in accordance with the terms of the Underwriting Agreement.

Based on the foregoing and subject to the assumptions, qualifications, limitations and exceptions set forth herein, we are of the opinion that, the Units, when issued and delivered to the Underwriters upon payment therefor in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by Sections 17-303, 17-607 and 17-804 of the Delaware Revised Uniform Limited Partnership Act (“DRUPLA”) and as described in the Prospectus).

The opinion expressed herein is limited in all respects to the DRUPLA, the Delaware Limited Liability Company Act (including, in each case, the applicable provisions of the Delaware Constitution and the reported judicial decisions interpreting these laws), the laws of the State of New York and the federal laws of the United States of America. We express no opinion as to the effect of the laws of any other jurisdiction, domestic or foreign.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Current Report on Form 8-K of the Partnership dated on or about the date hereof, to the incorporation by reference of this opinion into the Registration Statement and the reference to our firm under the heading “Legal Matters” in the Base Prospectus and the Prospectus Supplement. In giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the SEC issued thereunder.

Very truly yours,

/s/ Vinson & Elkins L.L.P.