Wyoming coach Dave Christensen was critical of the call.
"Guy's running off the field, 3 yards from the sidelines running off the field, takes his helmet off and you're going to throw a flag on him," Christensen said. "Kick him out of the game? That's unbelievable."
Smith was 21 of 34 for 197 yards and three touchdowns. His replacement, Jason Thompson, was 1 of 6 for 10 yards.
Nevada had the ball first in overtime, starting at the 25. After rushing for 1 yard on the first play, Combs hit Bradley cutting across the middle from 24 yards out.
Wyoming then took over at the 25 and after Thompson rushed for 1 yard on the first play, he threw three consecutive incomplete passes to end the game.
The Cowboys held Wolf Pack running back Stefphon Jefferson, the nation's leading rusher entering the game, to 78 yards on 23 carries, nearly 100 yards fewer than his season average of 174.
"I think our guys did a nice job stepping up against the run, but gave up far too many passing yards," Christensen said."