Robinson scored twice on the ground and twice with passes for the Wolverines (1-1), who sealed the win when defensive end Jake Ryan knocked down an Air Force pass with 1:28 left in the game.
Devin Funchess led Michigan's receivers with four grabs for 101 yards and a touchdown.
Devin Gardner chipped in with five receptions for 63 yards and a score for the victors.
Connor Dietz passed for 127 yards and added 61 rushing yards, but it wasn't enough for the Falcons (1-1).
Air Force got 130 rushing yards and three touchdowns from Cody Getz on 26 carries.