Austin Lopez had given the Spartans the lead on the first possession of overtime with a 35-yard field goal.
Nevada (6-4, 4-2 Mountain West Conference), getting the ball after a San Jose field goal with 2:49 to play, went 75 yards in 13 plays, scoring on Don Jackson's 2-yard run to tie the game at 31 with 36 seconds in regulation.
The Spartans (4-6, 3-3) got into position for a field goal on the final play but Ahki Muhammad blocked Lopez's 51-yard attempt.
Stewart completed 16 of 26 passes for 174 yards and James Butler ran for 119 yards and a score.
Kenny Potter threw for 186 yards and three touchdowns and ran for 116 yards for the Spartans.
The teams combined for 842 yards with no turnovers and just six penalties for 45 yards.