James Hamilton also scored a touchdown for North Texas (1-3), which amassed 257 rushing yards. Dodge was 10-for-15 passing for 146 yards in the Mean Green's first victory over Florida Atlantic (1-2) in the seven game series.
North Texas stretched its lead to 21-10 on Hamilton's 32-yard touchdown run in the fourth quarter, but the owls would close the gap on the ensuing possession. Jeff Van Camp's 36-yard touchdown pass to Rob Housler pulled Florida Atlantic within 21-17.
Florida Atlantic would threaten later marching to the Mean Green 28, but the North Texas defense stopped the potential game-winning drive.
Van Camp finished 20-for-31 for 273 yards.
Florida Atlantic took a 7-0 lead on a 1-yard touchdown run by Alfred Morris, but North Texas answered on the next possession. A 23-yard pass from Dodge to Carey capped an 9-play, 80-yard drive to tie it.
The Owls then pulled ahead on Ross Gornall's 30-yard field goal.
North Texas took its first lead of the game on a 46-yard touchdown pass from Dodge to Carey to make it 14-10.