The Mean Green (6-5, 5-0) have won 10 consecutive conference games and will play in the New Orleans Bowl for the second straight season on Dec. 17. New Mexico State (6-5, 4-1) would have ended a 42-year bowl drought with a victory.
With North Texas trailing 27-24, Taylor Casey forced Paul Dombrowski's fumble that Adrian Awasom recovered. On the next play, Galbreath gave North Texas the lead for good on a 19-yard touchdown run with 9:34 left. The Aggies then drove to the Mean Green 10, but Don McGee intercepted Dombrowski's pass in the end zone to end the threat.
New Mexico State had one final chance when it took over at its own 15. But Brandon Kennedy recovered Buck Pierce's fumble at the Aggies 1. Andrew Smith scored from there with 2:55 remaining to put the game away.
The Aggies took their last lead early in the fourth quarter when Dombrowski hit H.B. Briscoe on a 57-yard touchdown pass.
Dombrowski was 7-of-9 for 139 yards and two touchdowns. Pierce was 11-of-17 for 180 yards and a touchdown.
Briscoe had 105 yards receiving, and P.J. Winston added 101.
Galbreath became the first North Texas running back to post consecutive 1,000-yard rushing seasons.
New Mexico State, which led 20-14 at halftime, gained 440 yards against a North Texas defense that hadn't allowed a point in 12 quarters