The game kicked off the college boal season and marked the first post-season appearance for Memphis in 32 years.
Wimprine completed 10 of 11 passes for 162 yards in the opening half. He rushed for a seven-yard touchdown and tossed a 10-yard scoring strike to Chris Kelly, helping Memphis (9-4) build a 17-3 lead.
Wimprine finished 17 of 23 for 254 yards.
Patrick Cobbs, the nation's leading rusher, scored two touchdowns for North Texas (9-4) and finished with 110 yards -- 47 below his average.
With North Texas trailing, 17-10, Cobbs' 46-yard run was called back because of a holding penalty. It would have given the Mean Green a first down at the Memphis 13-yard line.