Quarterback Tim Jefferson ran for 94 yards and one score for Air Force (3-1, 2-0 MWC), but threw for 66 yards and was also intercepted once.
Alvester Alexander led the way for Wyoming (1-3, 0-1), rushing for 123 yards and two touchdowns in the loss.
After a scoreless first quarter the Cowboys took a 7-0 lead midway through the second stanza when Alexander plunged into the end zone on a one-yard run.
With just over two minutes remaining in the first half Air Force tied the game at seven with a four-yard touchdown run by Tew.
Alexander’s nine-yard touchdown run gave the Cowboys a 14-7 led early in the third frame.
Air Force capped off an impressive 16-play, 78-yard drive with a nine-yard touchdown run by Nathan Walker early in the final frame.
With just over three minutes remaining in regulation, Jefferson scampered into the end zone on a six-yard run, giving Air Force its first lead of the contest. However, the extra point was blocked, leaving the Falcons with just a 20-14 edge.
Wyoming was unable to regain the lead, as Air Force held on for the victory.