Hillman, a true freshman, toted the ball 24 times, and Ryan Lindley went 14-of-26 passing for 247 yards and a touchdown for the Aztecs (4-2, 1-1 MWC).
San Diego State's win was its first over a ranked foe since 1996.
Air Force (5-2, 3-1), meanwhile, saw its three-game winning streak snapped.
The Falcons' Tim Jefferson completed just 13-of-30 throws for 175 yards and a score. He rushed for 88 yards and Asher Clark added 116 yards and a touchdown on the ground.
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