Thompson completed 21-of-30 passes for 256 yards for the Mean Green (9-4), who played in a bowl game for the first time since 2004.
Brelan Chancellor carried the ball seven times for 47 yards and two scores for North Texas. He also hauled in six passes for 74 yards.
Caleb Herring connected on 22-of-41 passes for 196 yards, two touchdowns and an interception for the Rebels (7-6), who made their first bowl appearance since 2000. Herring also carried the ball 15 times for 33 yards.
The Rebels scored a touchdown on their first possession of the game. Herring completed all five of his passes on the drive, including a 9-yard TD pass to Marcus Sullivan.
North Texas got a bit of a break when UNLV's Keith Whitely fumbled a punt. The Mean Green took advantage of the mistake, as Antoinne Jimmerson scored on the ground from one yard out.
UNLV kicker Nolan Kohorst missed a 52-yard field goal as time expired in the first half.
The Mean Green scored a touchdown on their first possession of the second half. Marcus Smith's 27-yard catch on 3rd-and-7 led to Drew Miller's 7-yard TD catch.
North Texas put the game away with a 22-point fourth quarter. Chancellor's 3- yard TD run on the first play of the final period made it a 21-7 contest.
Darnell Smith capped a 10-play, 75-yard drive with a 34-yard touchdown catch.
Jerry Rice Jr. caught a 13-yard TD pass from Herring to get the Rebels within 28-14.
Chancellor's 15-yard TD run with 2:24 to play accounted for the final margin.
Despite the loss, the Rebels lead the all-time series with the Mean Green by a 4-1 margin ... North Texas won a bowl game for the first time since 2002 ... Darnell Smith caught five passes for 75 yards.