The only shot Mathis, who sank five 3-pointers, missed came at the buzzer of regulation.
Jahmel Taylor, who had 23 points, fueled a frenetic Bulldogs comeback, hitting four 3s in the final 4:24, including the shot that forced overtime with 18.1 seconds left.
"It was really good for us to get into a mucky game that could have gone either way and kind of bring back some memories of some other games and to pull it out and get a win," Lobos coach Paul Weir said. "We're not expecting any easy games in the tournament so to just go through another adverse situation is just another positive."
Simons, who had 16 points, and Antino Jackson, who scored four in overtime to also finish with 16, was too much for Fresno State (21-10, 11-7 Mountain West) in the extra session as the Lobos won their fifth-straight game.
New Mexico (17-14, 12-6) appeared to take control of the game near the end of the first half, going up 39-27 with raucous 15-3 run that included a steal and fastbreak layup plus one, another and-one moments later and an alley-oop dunk from Sam Logwood off a Mathis feed and capped by a Mathis 3-pointer.
But the Bulldogs ended the half on a 7-0 run to trail 39-34 at the break.
A 13-2 run restored New Mexico's advantage at 52-38 before the Bulldogs came back with a 10-0 surge of their own to pull within 54-50.
"We just kept working the game," Bulldogs coach Rodney Terry said. "We've been a resilient team all year long. We're going to play until the horn goes off. We're never going to stop playing. We just kept working the game for 40 minutes. Basketball is a game of runs. They had some runs, we withstood those. We came with runs ourselves and put ourselves in a position to win the game."
Taylor's backcourt mate, Deshon Taylor, also had 23 points, including 10 of 12 from the foul line.
Jahmel Taylor "made some incredible shots," Weir said. "I think we knew Deshaun Tayler, No. 21, could do all those things. But for Jahmel to be making those step-back 3s and all of that, that's some high level play. You have to give that backcourt credit. They fought."
With the win, New Mexico clinches third place in the conference.
The loss for Fresno State drops the Bulldogs to fourth place.
Coming into the game, New Mexico averaged 99 points in its four-game winning streak.
NO SEWING FOR TAYLOR
Bulldogs leading scorer Deshown Taylor had averaged eight points in Fresno State's last two games. He reached that total with a layup 12:11 into the first half and finished the half with 14.
WRINKLE IN TIME
With under a minute to play and New Mexico leading 81-78 and bringing the ball up court, play was stopped with the clock stuck on 40.3 seconds remaining. After a lengthy delay while officials checked monitors, play was restarted with 27.3 seconds remaining.
The Lobos earned a second-round matchup Thursday between the winner of the Wednesday's conference opener between sixth seed Wyoming and No. 11 seed San Jos� State. And, it puts New Mexico on the opposite of the bracket of top seed Nevada.
The Bulldogs slide to fourth seed to meet San Diego State on Thursday.
Iowa's Cook cleans up miss with strong dunk
Tyler Cook tracks down the missed layup and goes up to slam it home as it comes off the rim.
Eastern puts Morsell on skates
Purdue's Mojel Eastern collects the steal and breaks the ankles of Darryl Morsell before finishing at the cup.
Fernando drives and crushes the rim
Off the pick and roll, Bruno Fernando charges down the paint, catches the ball and slams it home to put Maryland up 29-25.