Exhibit 5.1

910 LOUISIANA
HOUSTON, TEXAS 77002-4995   TEL +1713.229.1234 FAX +1713.229.1522 BakerBotts.com AUSTIN
BEIJING BRUSSELS DALLAS DUBAI HONG KONG HOUSTON LONDON
MOSCOW NEW YORK PALO ALTO RIYADH SAN FRANCISCO WASHINGTON

August 16, 2019

CenterPoint Energy, Inc.

1111 Louisiana

Houston, Texas 77002

Ladies and Gentlemen:

As set forth in the Registration Statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by CenterPoint Energy, Inc., a Texas corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the sale from time to time pursuant to Rule 415 under the Act of up to 3,000,000 shares (the “Shares”) of common stock, par value $0.01 per share, of the Company (“Common Stock”) under the Company’s Fourth Amended and Restated Investor’s Choice Plan (the “Plan”), certain legal matters in connection with the Shares are being passed upon for you by us. At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

In our capacity as your counsel in the connection referred to above, we have examined originals, or copies certified or otherwise identified, of the Company’s Restated Articles of Incorporation and Third Amended and Restated Bylaws, each as amended to date, and the Plan, as amended to date, records of the Company, including certain resolutions of the Board of Directors of the Company, as furnished to us by the Company, certificates of governmental and public officials and of representatives of the Company, statutes and other instruments and documents as we have deemed necessary or advisable for purposes of the opinions hereinafter expressed.

In giving the opinions set forth below, we have relied, to the extent we deemed appropriate, without independent investigation or verification, upon certificates, statements, memoranda or other representations of officers, directors or other authorized representatives of the Company and of governmental and public officials with respect to the accuracy of the factual matters contained in or covered by such certificates, statements, memoranda or representations. In giving the opinions set forth below, we have assumed that all signatures on all documents examined by us are genuine, all documents submitted to us as originals are accurate and complete, all documents submitted to us as copies are true, correct and complete copies of the originals thereof, and all information submitted to us was accurate and complete.

On the basis of the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that:

1. The Company is a corporation duly incorporated and validly existing in good standing under the laws of the State of Texas.

2. With respect to Shares that are to be issued by the Company pursuant to the Plan as newly issued shares or to be sold by the Company pursuant to the Plan as treasury shares, such Shares have been duly authorized by all requisite corporate action on the part of the

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Company, and when so issued or sold from time to time in accordance with the terms and conditions of the Plan, including the receipt of any consideration provided for therein, assuming such consideration is not less than the par value of the Common Stock, such Shares will be validly issued, fully paid and nonassessable.

3. With respect to Shares that include shares of Common Stock which are issued and outstanding on the date hereof and are to be purchased in the open market on behalf of the Plan, such Shares have been duly authorized by all requisite corporate action on the part of the Company and will be validly issued, fully paid and nonassessable.

For the purposes of determining that previously issued shares of Common Stock will be duly authorized, validly issued, fully paid and nonassessable as contemplated by paragraph 3 above, (i) we have relied upon certificates of officers of the Company as to records of original issuances of Common Stock and as to the number of issued shares of Common Stock, (ii) as to the consideration received for such shares of Common Stock, we have relied on certificates of officers of the Company as to the Company’s actual receipt of the consideration provided for in the resolutions authorizing the issuance of such shares of Common Stock, and (iii) we have assumed that such previously issued shares of Common Stock that were issued pursuant to stock benefit plans or programs of the Company or upon conversion, exchange or exercise of any other security of the Company, or in certain circumstances a subsidiary of the Company, have been delivered either in accordance with the applicable stock benefit plan or program approved by the Board of Directors of the Company or upon conversion, exchange or exercise of any other security of the Company, or in certain circumstances a subsidiary of the Company, in accordance with the terms of such security or the instrument governing such security, providing for such conversion, exchange or exercise as approved by the Board of Directors of the Company.

The opinions set forth above in this letter are limited in all respects to matters of the laws of the State of Texas and applicable federal law. We hereby consent to the filing of this opinion of counsel as Exhibit 5.1 to the Registration Statement. We also consent to the references to our Firm under the heading “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ BAKER BOTTS L.L.P.