Exhibit 5.1

June 6, 2014

Piedmont Natural Gas Company, Inc.

4720 Piedmont Row Drive

Charlotte, NC 28210

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Piedmont Natural Gas Company, Inc., a North Carolina corporation (the “Company”), in connection with the preparation and filing by the Company with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-3, as may be amended from time to time (the “Registration Statement”), under the Securities Act of 1933, as amended, with respect to the potential offer and sale from time to time (the “Offering”), as set forth in the prospectus contained in the Registration Statement, of the following securities: (a) one or more series of senior or subordinated debt securities of the Company (the “Debt Securities”), (b) shares of the Company’s common stock, no par value per share (the “Common Stock”), (c) shares of the Company’s preferred stock, no par value per share (the “Preferred Stock”); (d) stock purchase contracts (the “Purchase Contracts”); (e) stock purchase contract units (“Purchase Contract Units”); (f) depositary shares (the “Depositary Shares”); and (g) warrants (the “Warrants”). The Debt Securities, Common Stock, Preferred Stock, Purchase Contracts, Purchase Contract Units, Depositary Shares and Warrants are hereinafter individually referred to as a “Security” and collectively referred to as the “Securities.”

The Debt Securities may be issued pursuant to a senior debt indenture, dated as of April 1, 1993 (the “Senior Indenture”), between the Company and The Bank of New York Mellon Trust Company, N.A. (as successor trustee to Citibank, N.A.) (the “Trustee”), or a subordinated debt indenture to be entered into between the Company and the Trustee, a form of which is attached as an exhibit to the Registration Statement (the “Subordinated Indenture” and, together with the Senior Indenture, each an “Indenture” and collectively, the “Indentures”).

The Purchase Contracts will be issued pursuant to one or more stock purchase contract agreements (each, a “Purchase Contract Agreement”) to be entered into between the Company and a financial institution identified therein as a purchase contract agent (each, a “Purchase Contract Agent”).

The Depositary Shares will be issued pursuant to one or more deposit agreements (each, a “Deposit Agreement”) between the Company and such depositary as shall be named therein (the “Depositary”).

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The Warrants will be issued under a warrant agreement (the “Warrant Agreement”) between the Company and a warrant agent as shall be named therein.

In rendering the opinions set forth herein, we have reviewed:

(1) the Articles of Incorporation of the Company, as amended to date;

(2) the Bylaws of the Company, as amended to date;

(3) the Certificate of Existence of the Company, dated as of June 6, 2014;

(4) the minutes of the October 16, 2013 meeting of the Board of Directors;

(5) the Registration Statement;

(6) the Company’s form of Common Stock certificate;

(7) the Senior Indenture;

(8) the Second Supplemental Indenture, dated as of June 15, 2003, between the Company and the Trustee;

(9) the Third Supplemental Indenture, dated as of June 20, 2006, between the Company and the Trustee;

(10) the Fourth Supplemental Indenture, dated as of May 6, 2011, between the Company and the Trustee; and

(11) the form of Subordinated Indenture.

We have also reviewed such other documents and considered such matters of law and fact as we, in our professional judgment, have deemed appropriate to render the opinions contained herein. With respect to certain facts, we have considered it appropriate to rely upon certificates or other comparable documents of public officials and officers or other appropriate representatives of the Company without investigation or analysis of any underlying data contained therein.

In rendering the opinions set forth herein, we have assumed that: (1) upon the issuance of any Common Stock or Preferred Stock, including upon the exercise, conversion or exchange of any convertible Security, the total number of shares of Common Stock or Preferred Stock issued and outstanding will not exceed the total number of shares of Common Stock or Preferred Stock, as applicable, that the Company is then authorized to issue under its Articles of Incorporation, as then in effect, and other relevant documents; (2) at the time of execution, authentication, issuance and delivery of the Debt Securities, the related Indenture will be the valid and legally binding obligation of the Trustee thereunder; (3) at the time of execution, authentication, issuance and delivery of subordinated debt securities, the Subordinated Indenture will have been duly authorized, executed and delivery by the Company; (4) at the time of execution, issuance and delivery of the related Purchase Contracts, the Purchase Contract Agreement will be the

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valid and legally binding obligation of the related Purchase Contract Agent and will have been duly authorized, executed and delivered by the Company; (5) at the time of execution, authentication, issuance and delivery of the Depositary Shares, the related Deposit Agreement will be the valid and legally binding obligation of the Depositary and will have been duly authorized, executed and delivered by the Company; (6) at the time of execution, countersignature, issuance and delivery of the Warrants, the related Warrant Agreement will be the valid and legally binding obligation of each party thereto other than the Company and will have been authorized, executed and delivered by the Company; (7) at the time of execution, countersignature and delivery of any Purchase Contract Units that include debt obligations of third parties (including U.S. Treasury securities), such debt obligations of third parties will be the valid and legally binding obligation of such third parties, and the indenture relating to such debt obligations will be the valid and legally binding obligation of such third parties and each trustee party to such indenture, enforceable against such third parties and trustee parties in accordance with its terms, and that such third parties and trustee parties will comply with all of their obligations under such indenture and all laws applicable thereto; and (8) any Purchase Contract Agreement, Deposit Agreement or Warrant Agreement will be governed by the laws of the State of North Carolina or the State of New York.

The opinions set forth herein are limited to matters governed by the laws of the State of North Carolina and the State of New York, and no opinion is expressed herein as to the laws of any other jurisdiction. Without limiting the generality of the foregoing, we express no opinion with respect to state securities or “Blue Sky” laws. We express no opinion concerning any matter respecting or affected by any laws other than laws that a lawyer in North Carolina exercising customary professional diligence would reasonably recognize as being directly applicable to the Company and the transactions contemplated by this opinion.

Based upon and subject to the foregoing and the further assumptions, limitations and qualifications hereinafter expressed, it is our opinion that:

(1) with respect to the Debt Securities, assuming (a) the taking of all necessary corporate action to authorize and approve the issuance and terms of any Debt Securities, the terms of the offering thereof and related matters by the Board of Directors of the Company or a duly acting and constituted committee thereof (such Board of Directors or committee being referred to herein as the “Board”) or duly authorized officers of the Company (such Board or authorized officers being referred to herein as the “Authorizing Party”) and (b) the due execution, authentication, issuance and delivery of such Debt Securities, upon payment of the consideration therefor provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Authorizing Party and otherwise in accordance with the provisions of the applicable Indenture and such agreement, such Debt Securities will constitute valid and legally binding obligations of the Company;

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(2) with respect to the Common Stock, assuming (a) the taking by the Board of all necessary corporate action to authorize and approve the issuance of the Common Stock, the terms of the offering thereof and related matters and (b) the issuance and delivery of the Common Stock, upon payment therefor in accordance with the applicable purchase, underwriting or similar agreement approved by the Board, the Common Stock will be validly issued, fully paid and non-assessable;

(3) with respect to the Preferred Stock, assuming (a) the taking by the Board of all necessary corporate action to authorize and approve the issuance of the Preferred Stock, the terms of the offering thereof and related matters, (b) due filing of the Certificate of Designations in accordance with the Company’s Articles of Incorporation and the North Carolina Business Corporation Act and (c) due issuance and delivery of the Preferred Stock, upon payment therefor in accordance with the applicable definitive purchase, underwriting or similar agreement approved by the Board, the Preferred Stock will be validly issued, fully paid and non-assessable;

(4) with respect to the Purchase Contracts, assuming (a) the taking of all necessary corporate action by the Board to authorize and approve the execution and delivery of a related Purchase Contract Agreement, the terms of the offering thereof and related matters by the Board and (b) the due execution, issuance and delivery of the Purchase Contracts, upon payment of the consideration for such Purchase Contracts provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board and otherwise in accordance with the provisions of the applicable Purchase Contract Agreement and such agreement, the Purchase Contracts will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms;

(5) with respect to the Purchase Contract Units, assuming (a) the taking of all necessary corporate action by the Authorizing Party to authorize and approve (1) the issuance and terms of the Purchase Contract Units, the terms of the offering thereof and related matters and (2) the issuance and terms of the Securities that are a component part of the Purchase Contract Units, the terms of the offering thereof and related matters and (b) the due execution, countersignature, authentication, issuance and delivery of each Security that is a component of the Purchase Contract Unit, in each case upon the payment of the consideration therefor provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Authorizing Party and otherwise in accordance with the provisions of the applicable unit agreement and such agreement, the Purchase Contract Units will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms;

(6) with respect to the Depositary Shares, assuming (a) the taking of all necessary corporate action by the Board to authorize and approve (1) the issuance and terms

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of the Depositary Shares, the terms of the offering thereof and related matters and (2) the execution and delivery of the Deposit Agreement, (b) the Preferred Stock represented by the Depositary Shares has been duly delivered to the Depositary under the Deposit Agreement and (c) the due execution, issuance and delivery of the depositary receipts evidencing the Depositary Shares, against deposit of the Preferred Stock in accordance with the Deposit Agreement, upon payment of the consideration therefor provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board, the depositary receipts evidencing the Depositary Shares will be validly issued and will entitle the holders thereof to the rights specified in the Depositary Shares and the Deposit Agreement; and

(7) with respect to the Warrants, assuming (a) the taking of all necessary corporate action by the Board or, in the case of Warrants for the purchase of debt securities, the Authorizing Party, to authorize and approve the execution and delivery of a related Warrant Agreement and (b) the due execution, countersignature, issuance and delivery of such Warrants, upon payment of the consideration for such Warrants provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board or, in the case of Warrants for the purchase of debt securities, the Authorizing Party, and otherwise in accordance with the provisions of the applicable Warrant Agreement and such agreement, such Warrants will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms.

The opinions expressed herein are subject to the following qualifications (i) applicable bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws (or related judicial doctrines) now or hereafter in effect affecting creditors’ rights and remedies generally; and (ii) general principles of equity including, without limitation, standards of materiality, good faith, fair dealing and reasonableness, equitable defenses and limits as to the availability of equitable remedies, whether such principles are considered in a proceeding at law or in equity.

Our opinions expressed herein are as of the date hereof, and we undertake no obligation to advise you of any changes in applicable law or any other matters that may come to our attention after the date hereof that may affect our opinions expressed herein.

We understand that we may be referred to as counsel who has passed upon the legality of the Securities on behalf of the Company in the Registration Statement, and we hereby consent to such use of our name in the Registration Statement and to the use of this opinion for filing with

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the Registration Statement as Exhibit 5.1 thereto. The filing of this consent shall not be deemed an admission that we are an expert within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Parker Poe Adams & Bernstein LLP

RDH/VLC/EWW