Freshman Rasheed Sulaimon added 19 points and Ryan Kelly had 14 points for the Blue Devils (3-0).
They scored 30 straight points—including a 23-0 run to close the first half—to brush off a slow start, and forced 25 turnovers to cruise in this preliminary on-campus matchup in the Battle 4 Atlantis tournament.
Bernard Thompson scored a career-high 24 points for Florida Gulf Coast (2-2), which led for most of the first half.
But foul trouble, sloppy ball-handling and cold shooting during the last 5 1/2 minutes of the half ruined the Eagles' chances at their first win over a Top 25 team and second victory in six days against an Atlantic Coast Conference program.
Sherwood Brown added 12 points for Florida Gulf Coast, which finished with more turnovers than field goals (23) and never got closer than 19 in the second half.
Plumlee surpassed his previous best of 25 points set as a sophomore against Marquette in 2010. He's a 51 percent free-throw shooter, but he was 10 of 11 from the foul line—by far his best night from the stripe when he's gone there at least 10 times.
Seth Curry added 10 points for the Blue Devils, who were playing five days after beating No. 3 Kentucky in Atlanta and four days before taking on Minnesota in the Bahamas. They overcame 18 turnovers by turning the Eagles' miscues into 36 points.
They haven't lost a nonconference game at Cameron Indoor Stadium since 2000, and surpassed their previous mark of 95 straight non-ACC wins here, set from 1983-95.
Yet for a while, this latest streak sure looked like it was in jeopardy.
The Eagles, who beat Miami by 12 on Nov. 13, led for much of the way early behind some sharp 3-point shooting. Florida Gulf Coast hit 6 of its first 12 from beyond the arc and took a 30-29 lead on Filip Cvjeticanin's 3 with 5 1/2 minutes before the break.
That's when Duke finally got rolling. Guard Quinn Cook, who made his first start of the season, hit his second straight 3 a few seconds later to put the Blue Devils ahead to stay and start the overwhelming run.
Kelly scored seven points during the burst while Cook ended it with a jumper with about 7 seconds left to make it 52-30.
The Blue Devils then scored the first seven points of the second half, going up 59-30 on Plumlee's free throw with 18:34 left.