Swanson's game-winner was his second touchdown of the day and came with the score tied 35-35. He had 97 yards for the Rockets (5-3, 4-0 Mid-American). Kareem Hunt ran for 198 yards and a score and Logan Woodside passed for 225 yards and three touchdowns.
In the third, Woodside threw a 42-yard scoring strike to Corey Jones. Hunt later scored from 36 yards to give Toledo its first lead of the game, 28-20.
Woodside and Frohnapfel traded touchdown passes in the fourth quarter to tie the game 35-35 with 5:57 left.
Frohnapfel threw for 438 yards and five touchdowns for the Minutemen (2-7, 2-3).