A third freshman, Josh Quezada, ran for 107 yards and a touchdown as the Cougars (6-5, 5-2 Mountain West) won for the fifth time in six games despite committing 14 penalties.
Stump Godfrey threw for 125 yards and a touchdown and added 53 yards rushing for New Mexico (1-10, 1-6).
Heaps threw a 17-yard touchdown pass to Hoffman in the third quarter and a 10-yarder in the fourth quarter. Heaps finished 18-of-32 for 231 yards.
Mitch Payne made two field goals and four extra points to become the Mountain West career leader in kicking points with 314, two more than his brother Matt had for BYU.
Less than four months removed from his transfer to Florida State, Everett Golson has been named the Seminoles' starting quarterback.
After hinting at it for more than a week, LSU coach Les Miles confirmed Monday that Brandon Harris will start at quarterback in Saturday's opener against McNeese State.
USC AD Pat Haden said he had "thoughtful conversations" with medical professionals and that "a lot of careful thought was given" before deciding on a course of action for coach Steve Sarkisian.
A final decision in Ohio State's quarterback derby won't be revealed until just before the season kicks off, but Urban Meyer isn't ruling out playing both his decorated candidates.
With less than a week to go before the season opener, No. 9 Georgia finally has a starting quarterback. Coach Mark Richt announced Monday that Greyson Lambert had won the starting job.
Sales of beer with Joe Paterno's name on it are so brisk that the company that makes it is gearing up for a second run after just a week on the shelves.