Pegram scored on a 54-yard run on the second play from scrimmage. Later in the first quarter, Andrew McNulty connected with Marcus Smith for a 4-yard score to give the Mean Green a 14-0 lead.
McNulty was 9 of 20 for 105 yards for North Texas (4-7, 2-5 Conference USA).
Alex McGough completed 11 of 25 passes for 56 yards and three interceptions for FIU (4-8, 3-5 C-USA). Anthon Samuel had 89 yards on the ground as the Golden Panthers were held to 147 total yards.
FIU's Richard Leonard scored on a 71-yard punt return to pull within 14-7 and Jeremiah McKinnon returned an interception 71 yards to even the score at 14 at halftime.
Trevor Moore kicked a 36-yard field goal at the end of the third quarter for the deciding points.