Exhibit 5.1

		300 Colorado Street, Suite 2400
		Austin, TX 78701
		Tel: +1.737.910.7300 Fax: +1.737.910.7301
		www.lw.com
		FIRM / AFFILIATE OFFICES
		Austin		Milan
		Beijing		Munich
		Boston		New York
		Brussels		Orange County
		Chicago		Paris
		Dubai		Riyadh
April 15, 2026		Düsseldorf		San Diego
		Frankfurt		San Francisco
		Hamburg		Seoul
		Hong Kong		Silicon Valley
		Houston		Singapore
		London		Tel Aviv
		Los Angeles		Tokyo
		Madrid		Washington, D.C.

Tamboran Resources Corporation

Level 39, Suite 1, Tower One

100 Barangaroo Avenue

Barangaroo NSW 2000, Australia

To the addressee set forth above:

We have acted as special counsel to Tamboran Resources Corporation, a Delaware corporation (the “Company”), in connection with the issuance of 96,698 shares of common stock, $0.001 par value per share (the “Shares”). The Shares are included in an automatic shelf registration statement on Form S-3 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on April 7, 2026 (Registration No. 333-294908, as amended, the “Registration Statement”), a base prospectus dated April 7, 2026 (the “Base Prospectus”) and a prospectus supplement dated April 7, 2026 filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”). The Shares are being sold pursuant to share purchase agreements dated as of April 8, 2026 by and between the Company and the purchasers named therein (the “Purchase Agreements”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related Prospectus, other than as expressly stated herein with respect to the issue of the Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to the applicability thereto, or the effect thereon, of the laws of any other jurisdiction or, in the case of Delaware, any other laws.

April 15, 2026

Page 2

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof, when the Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the purchasers, and have been issued by the Company against payment therefor (not less than par value) in the circumstances contemplated by the Purchase Agreements, the issue and sale of the Shares will have been duly authorized by all necessary corporate action of the Company, and the Shares will be validly issued, fully paid and nonassessable. In rendering the foregoing opinion, we have assumed that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Company’s Form 8-K dated April 15, 2026 and to the reference to our firm in the Prospectus under the heading “Legal Matters.” In giving such consent, we do not thereby 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.

Sincerely,

/s/ Latham & Watkins LLP