Five different Lobos scored on the ground while Carlos Wiggins added a touchdown catch and took a kickoff back for another score as New Mexico (2-3) equaled its highest point total in the series with the Aggies (0-6).
"It's good to get a win," said New Mexico coach Bob Davie. "It was a big win for us. There's no hiding that."
Carrier finished with 126 yards on 14 carries, and Lobos quarterback Cole Gautsche added 127 yards on 12 carries with one touchdown rushing and one passing.
"Really momentum came on our side very quick," Carrier said. "And our o-line just dominated from the start and didn't let up the whole game."
Demarcus Rogers, Crusoe Gongbay and Jhurell Pressley also added scoring runs for the Lobos (2-3), who finished with 541 yards on the ground.
That depth and speed on the corners coupled with Gautsche effectively running the option opened holes inside for Carrier.
"It makes everything a lot easier because now the safeties aren't thinking about staying in the box," he said. "They know they have to roll with the guy coming in motion.
Brandon Betancourt led the Aggies with 139 yards on 23 carries, but he lost a fumble. New Mexico State quarterback Andrew McDonald ran for one score and threw for another while going 19 of 33 for 262 yards and two interceptions.
"These fifth-year seniors had never beaten this team in this stadium," Davie said. "And that was significant."
A week after allowing 56 points and 568 total yards, the Lobos defense responded, led by defensive end Brett Bowers, who had three sacks and forced a fumble.
"I've just a got a big smile on my face," he said. "We played a lot better. We definitely picked it up, did our job and made some plays."
New Mexico State didn't help its cause very much with three turnovers and a failure to move the ball early as it fell behind 21-0.
"We are stagnant offensively right now," Aggies coach Doug Martin said. "We just don't have guys making plays."