Exhibit 32.1

Certification of Chief Executive Officer and Chief Financial Officer

Pursuant to 18 U.S.C. Section 1350

As Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report of Rosetta Resources Inc. (“the Company”) on Form 10-Q for the period ended June 30, 2015 (“Form 10-Q”), each of the undersigned officers of the Company certifies pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that to the best of such officer’s knowledge: (i) the Form 10-Q fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.