Exhibit 5.1

910 LOUISIANA
HOUSTON, TEXAS
77002-4995   TEL +1 713.229.1234 FAX +1 713.229.1522 BakerBotts.com AUSTIN BRUSSELS DALLAS DUBAI HOUSTON LONDON NEW YORK PALO ALTO RIYADH SAN FRANCISCO SINGAPORE WASHINGTON

August 8, 2024

CenterPoint Energy, Inc.

1111 Louisiana Street

Houston, Texas 77002

Ladies and Gentlemen:

In connection with the issuance by CenterPoint Energy, Inc., a Texas corporation (the “Company”), of 9,754,194 shares (the “Shares”) of common stock, par value $0.01 per share, of the Company, pursuant to (a) the Registration Statement on Form S-3, Registration No. 333-272025 (the “Registration Statement”), which was filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), and (b) the related prospectus of the Company dated May 17, 2023, as supplemented by the prospectus supplement of the Company relating to the sale of the Shares dated August 7, 2024 (as so supplemented, the “Prospectus”), as filed by the Company with the Commission pursuant to Rule 424(b) under the Act, certain legal matters with respect to the Shares are being passed upon for you by us. At your request, this opinion letter is being furnished to you for filing as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be filed with the Commission on the date hereof (the “Form 8-K”).

The Shares are being offered, issued and sold pursuant to the Underwriting Agreement dated August 7, 2024 (the “Underwriting Agreement”), by and among the Company and the several underwriters named in Schedule I thereto (the “Underwriters”).

In our capacity as your counsel in the connection referred to above, we have examined originals, or copies certified or otherwise identified, of (i) the Restated Articles of Incorporation of the Company and the Fourth Amended and Restated Bylaws of the Company (each as amended to date, the “Organizational Documents”); (ii) the Underwriting Agreement; (iii) the Registration Statement and the Prospectus; and (iv) corporate records of the Company, including certain resolutions of the board of directors of the Company, as furnished to us by you, certificates of 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 opinion hereinafter expressed. In giving the opinion set forth below, we have relied, to the extent we deemed appropriate without independent investigation or verification, upon certificates, statements or other representations of officers 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 or representations. In giving the opinion below, we have assumed that all signatures on all documents examined by us are genuine, all documents submitted to us as originals are authentic and complete, all documents submitted to us as certified or photostatic copies are true, correct and complete copies of the originals thereof and all information submitted to us was accurate and complete.

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On the basis of the foregoing, and subject to the limitations and qualifications set forth herein, we are of the opinion that the Shares have been duly authorized by all necessary corporate action on the part of the Company, and, when issued and delivered by the Company against payment of the purchase price therefor in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and non-assessable.

The opinion set forth above is limited in all respects to matters of the laws of the State of Texas and applicable federal law of the United States, in each case as in effect on the date hereof. We express no opinion as to the effect of the laws of any other jurisdiction. We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Form 8-K. We also consent to the references to our Firm under the heading “Legal Matters” in the Prospectus. 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.