Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002,

18 U.S.C. SECTION 1350

In connection with the Quarterly Report on Form 10-Q of Tamboran Resources Corporation (the “Company”) for the quarter ended September 30, 2025, as filed with the U.S. Securities and Exchange Commission on the date hereof (the “Report”), I, Richard Stoneburner, Interim Chief Executive Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that, to my knowledge:

The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: November 13, 2025

/s/ Richard Stoneburner

Richard Stoneburner

Interim Chief Executive Officer and Director

(Principal Executive Officer)