"We were looking for it all game," Lamb said of the fake punt. "They either bring a lot of rush or block a lot of people. We saw that they were trying to block."
Both teams are 3-4, and 2-2 in the Big Sky Conference.
"To lose here at home is very disheartening," said Montana coach Mick Delaney. "One thing that's very obvious is that we cannot finish in the second half."
The Grizzlies jumped out to a 17-13 halftime lead behind a 6-yard pass from Trent McKinney to Clay Pierson, McKinney's 2-yard scoring run and Chris Lider's 43-yard field goal.
The Thunderbirds rebounded in the second half, going ahead 20-17 on a 2-yard run by Brad Sorensen with 5 minutes left in the third quarter.
Montana knotted the score at 20 when Lider kicked a 42-yard field goal with 7:58 remaining.
But on fourth-and-2, Miller saw the entire Grizzly defense drop back to block and took off down the left sideline to the Montana 27-yard line.
"We felt if we needed it, it would be there," Lamb said.
After Montana turned the ball over on downs, Myles Crawford-Harris ran the ball 34 yards for a touchdown to seal the victory for the Thunderbirds.
Sorensen completed 30 of 53 passes for 294 yards. He connected on first-half touchdown passes of 7 yards to Fatu Moala and 20 yards to Henna Brown. Sorensen was also sacked seven times by the Montana defense.
"I don't think I will be able to move tomorrow," Sorensen said after the game. "I'm pretty sore right now."
Moala hauled in a game-high 11 catches for 104 yards.
McKinney finished the game 17 of 29 for 194 yards and one touchdown. Montana's Peter Nguyen led all rushers with 91 yards on 15 carries.