But Utah State (3-8, 2-6) drove 51 yards on nine plays to setup Hamblin's game winning effort.
Gill completed a 21-yard pass to Paul Dombrowski on fourth and 10 from the New Mexico State 20-yard line, but Gill's fourth down pass from the NMSU 41-yard line was intercepted by Terrance Washington with 25 seconds left to play to seal the outcome.
Gill finished 10-17 for 92 yards while starter Joey Gill, who played the first three quarters, completed 20 of 32 passes for 214 yards and a score.
Justine Buries led the NMSU rushing attack with 85 yards on 22 carries and a touchdown.
Paul Dombrowski had eight catches for 106 yards to lead New Mexico State.
Utah State quarterback Jerod Walker ran 25 times for 102 yards and completed 14 of 20 passes for two touchdowns and 182 yards.
New Mexico State had 423 total yards to 395 for Utah State.
Senior linebacker Jimmy Cottrell ended his spectacular career in fine fashion with a career-high 25 tackles, just one short of the school record for most tackles in a game.
He finished the season with 179 tackles, breaking the old school record of 169 set by Sam Dickey in 1989.
Dombrowski finished the season with 78 catches for 798 yards. He broke the school record for catches in a season last week against San Jose State.
Cottrell finished his career with 463 total tackles, third best in school history.
Utah State took a 7-0 lead on their first possession of the game, after recovering an NMSU fumble at their won 34-yard line. Ryan Bohm scored on a 1-yard touchdown plunge.
New Mexico State answered back on the next possession as NMSU drove 65 yards on 13 plays with Buries scoring from two yards out to tie the game with just over seven minutes left in the first quarter.
On NMSU's second drive of the second quarter, Vincent completed a perfectly timed 11 yard touchdown pass to freshman running back Jeremiah Williams on third and goal to give the Aggies a 14-7 lead with 8:28 left in the game. The key play came on a 40-yard completion from Vincent to Nick Cleaver.
Utah State came right back and drove 65 yards on four plays with Walker hitting Tony Pennyman on a 40-yard touchdown pass to tie the score at 14.
Neither team scored in the third quarter, but Utah State scored on the first play of the fourth quarter as Walker hit Pennyman on a 10-yard scoring pass on third and four.
NMSU had put together five consecutive scoreless drives before changing quarterbacks and brining in Gill for the first NMSU drive of the fourth quarter.
The key plays of the game-tying drive included a 16-yard completion from Gill to Allen on third and five from the Utah State 47-yard line and a 21-yard completion from Gill to Tim Tolbert down to the Utah State five yard line to set up the game tying score.
Two other seniors finished their careers with double figures in tackles as Matt Griebel had 13 and John Howell finished with 11. Griebel finished the season with 149 tackles, a career high.