Jack-of-all-trades Brandon Connette ran for one score and threw for another, and Ross Cockrell returned a blocked field goal 75 yards for the TD that capped the Blue Devils' most productive quarter since 1999.
Renfree was 21 of 30. Conner Vernon had 10 catches for 180 yards and a 28-yard TD, and set a school record with his 208th career reception.
Duke opened by beating a Football Bowl Subdivision team for the first time since 2002. The Blue Devils led 44-14, improved to 3-2 in openers under David Cutcliffe and snapped a seven-game losing streak that dated back to last year's victory over FIU.
Kedrick Rhodes rushed for 130 yards and had a 67-yard touchdown catch and a short, late scoring run.
This one was all but over at halftime after a big special teams play by the Blue Devils produced a 10-point swing and a huge shift in momentum.
FIU drove to the Duke 13 in the final seconds of the half and lined up for a 30-yard field goal that would have cut the deficit to 13 points. Austin Gamble blocked Jack Griffin's kick, and Cockrell scooped up the ball and cut across the field to put Duke up 37-14.
That capped the Blue Devils' highest-scoring half since rolling up 41 points in the first half of a 1999 win against Wake Forest. That's also the last time they scored at least 30 points in a quarter.
Connette, a backup and short-yardage quarterback who also lines up at receiver and tight end, had a 2-yard scoring run midway through the first quarter before getting that huge second quarter started on the first play — his 8-yard touchdown pass to David Reeves.
Long passes from Renfree to Vernon set up consecutive second-quarter scores. A 46-yard completion came one play before Connette's TD pass, and Vernon's 49-yard catch-and-run was followed two plays later by Josh Snead's 19-yard scoring run that made it 20-7.
Cockrell's big return made it a stress-free second half. The only thing in doubt was whether Vernon would get to Donovan Varner's career receptions record — which he did midway through the fourth.
Jake Medlock was 27 of 45 for 348 yards with two touchdowns for the Panthers, the favorites in the Sun Belt.
Their star from last year — big-play receiver T.Y. Hilton — is in the NFL, but they do still have Rhodes, who finished with 115 yards receiving on seven catches. He set the school's single-season rushing record in 2011 and struck for a score 43 seconds into the 2012 season by taking a quick pass from Medlock and racing for his long TD.
At one point midway through the second quarter, FIU had 189 total yards — and Rhodes was responsible for 150 of them.
Darian Mallary's 10-yard touchdown run late in the second pulled FIU to 20-14, but that was as close as the Panthers could get.
Rhodes scored from 1 yard out with 1:19 remaining, but Kyler Brown intercepted Medlock's conversion pass and returned it 98 yards to make it 46-20.