Jackson, a freshman, came off the bench to replace injured Taylor McHargue in the second quarter and completed 15-of-21 passes for Rice (7-6) -- which overcame a 14-7 halftime deficit thanks to his two TD passes, a pair of Chris Boswell field goals and a 22-yard touchdown run by Charles Ross.
Jordan Taylor caught three TD passes for the Owls, who had to win their final four games of the regular season to become bowl eligible.
Air Force (6-7) was held to just two first downs in the second half and ran for 166 yards in the game, about half of the what the Falcons averaged in the regular season.
Kale Pearson and Wes Cobb ran for the two Air Force scores in the second quarter. Pearson, one of three quarterbacks used by Air Force in the game, completed 2-of-8 passes for 44 yards and was intercepted once.