The Blue Devils (3-2) rallied from a 10-point deficit early in the fourth quarter and took the lead on Thompson's 9-yard run with 6:52 remaining. On the previous play, Jordan DeWalt-Ondijo sacked Panthers quarterback Wesley Carroll, forcing a fumble. Anthony Young-Wiseman recovered the fumble at the Florida International 17 and ran it to the 9-yard line.
The Panthers (3-2) drove to the Blue Devils 12, but Carroll's fourth-down pass to T.Y. Hilton in the end zone fell incomplete with 2:29 remaining.
Carroll threw his third touchdown pass with 13:30 remaining in the fourth quarter to put the Panthers ahead 27-17. Carroll connected with Wayne Times on a 34-yard catch and run.
Renfree completed 28 of 43 passes for 336 yards and two touchdowns while Carroll finished 26 of 40 for 328 yards.
The teams exchanged leads twice during a 31-point first quarter.
Florida International erased a 3-0 deficit on one play as Carroll connected with Hilton for a 63-yard play action touchdown pass and a 7-3 lead.
The Blue Devils countered and regained the lead 14-10 with a 5-play, 68-yard drive capped by Renfree's 31-yard touchdown pass to Vernon. Vernon finished with eight receptions and 117 yards.
Duke's lead was short-lived as Carroll's 15-yard touchdown pass to Jonathan Faucher culminated a 10-play, 85-yard drive and gave the Panthers a 14-10 advantage.
Renfree threw his second touchdown pass on the next Duke drive when he connected with Cooper Helfet for 22 yards and gave the Blue Devils a 17-14 lead late in the quarter.
Renfree completed 12 of 14 passes for 173 yards in the first quarter and Carroll was 9-of-12 for 157 yards.
The scoring subsided in the second quarter. Florida International kicker Jack Griffin scored the only points of the quarter on a 36-yard field goal with 4:01 remaining to tie it at 17.