Jefferson finished with 111 passing yards and 64 yards on the ground for Air Force (8-4, 5-3 MWC), which has won its last four meetings with UNLV.
Omar Clayton passed for 224 yards and one touchdown in defeat for UNLV (2-9, 2-5).
Air Force jumped out to 7-0 lead just over two minutes into the game when Jefferson threw a five-yard touchdown pass to Zach Kauth.
UNLV then scored 17 unanswered points to give the Rebels a 17-7 advantage by the middle of the second quarter. Tim Cornett got things going with a two-yard touchdown run, and after a 32-yard field goal by Nolan Kohorst, Clayton threw a 36-yard scoring pass to Phillip Payne.
With less than two minutes left in the first half, the Falcons cut their deficit to 17-14 on a one-yard touchdown plunge by Jefferson.
The Falcons came out hot in the third quarter, scoring two more touchdowns to regain the lead at 28-17. A 54-yard scoring scamper by Jonathan Warzeka was followed by a two-yard rushing touchdown by Jefferson.
UNLV made the score 28-20 with a 32-yard field goal by Kohorst.
With just under 10 minutes left in the game, Air Force pushed its advantage to 35-20 with another Jefferson touchdown run, this time from two yards out.