Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (No. 333-288382, 333-293057 and 333-294908) and Form S-8 (No. 333-280558 and 333-296575) of Tamboran Resources Corporation of our report dated August 6, 2026, relating to the consolidated financial statements of Falcon Oil & Gas Ltd.(the “Company”) which appear in this Form 8-K/A. Our report contains an explanatory paragraph regarding the Company’s ability to continue as a going concern.

/s/ BDO Canada LLP

Calgary, Alberta

August 7, 2026