Carr threw a 64-yard touchdown pass to Adams on the Bulldogs' second play from scrimmage and 1:46 later hooked up with Isaiah Burse for a 36-yard score.
Marcel Jensen added two 1-yard touchdown catches, one from Carr and one from tailback Robbie Rouse for Fresno State.
The Bulldogs (9-3, 7-1) share the MWC title with San Diego State, which defeated Wyoming 42-28 on Saturday. Boise State can make it a three-way split by defeating Nevada next Saturday.
Cody Getz had 82 rushing yards and Jon Lee added 52 for Air Force (6-6, 5-3), which finished with 254 rushing yards and just 63 passing.