The Grizzlies (5-5, 3-4 Big Sky) led 10-7 at halftime, but Weber State took the lead on Kris Parham's 1-yard run in the third quarter before Montana rallied.
The Wildcats (1-8, 1-5) closed in after Chris Lider's third field goal, a 35-yarder, made it 24-14 Montana. Cordero Dixon returned the kickoff 100 yards for a score with 3:41 to play, but Weber State never got the ball back.
Peter Nguyen ran for 103 yards for Montana, which won consecutive games for the first time this season. The Grizzlies have one game remaining, at home against Montana State in two weeks. Weber State's only win of the season came in its previous game, two weeks ago at Southern Utah.