The Wildcats (7-1, 4-1 Big Sky Conference), ranked seventh in the FCS coaches poll, took a 24-13 lead on Barron's second TD pass, a 12-yarder to Hayden Meacham with 5:56 to play.
But Malik Flowers took the ensuing kickoff 100 yard s and the Grizzlies (5-3, 2-3), who have lost three straight and dropped to 10th in the rankings, used a trick play for the 2-point conversion to pull within a field goal.
Weber State then pounded the ball on the Grizzlies and clinched the game by converting a fourth-and-1 just outside the Montana 40.
Barron was 14-of-23 passing for 153 yards and Dontae McMillan ran for 100 on 23 carries. Damon Bankson added 79 yards on nine carries, including a 47-yard touchdown for a 7-3 lead. Bronson's first TD was a 69-yard catch-and-run with Ty MacPherson to grab a 17-13 lead in the third quarter.
Montana could only muster 114 yards behind backup quarterback Kris Brown. Brown was just 10-of-17 passing for 72 yards and was sacked four times as the replacement for Lucas Johnson, who was injured early in last week's overtime loss to third-ranked Sacramento State.
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