Nolan Smith contributed 21 points, including 5-of-10 from beyond the arc, for the Blue Devils (22-4, 10-2 ACC), who won their fifth straight game. Jon Scheyer added 15 points, and Brian Zoubek 10 with five rebounds and five steals.
Duke reeled off the first seven points of the second half, and after Scheyer drained one from long distance, the game was tied, 39-39, less than four minutes in.
The visitors continued to surge, taking a 47-42 lead on a Mason Plumlee slam, then went ahead 54-46 on a Smith three just prior to the midway point of the half.
Miami clawed back within to 54-52 with 8:39 to play on a Scott bucket, then came within 56-55 two minutes later on a Dews fast-break layup.
Scheyer's trey from the top of the key put Duke ahead 61-57 with 5:29 left in regulation, and Duke began to pull away for good. He drilled another three, then Zoubek hit two free throws before Smith knocked down a three to make it 69-59 with 3:11 remaining.
The Hurricanes got as close as five, 77-72, with under 20 ticks left, but by then it was too late.
Singler's three put Duke up 6-4 early, but the Hurricanes blitzed the visitors with a 20-8 run, ending when Dews hit 1-of-2 from the line for a 24-14 game.
Two buckets by Zoubek brought the Blue Devils within six, but Miami quickly established a 32-22 advantage on an Adrian Thomas free throw. Smith's trey was countered by a three from Thomas, and Scott's bucket gave the home team a 12- point lead at the break.
Duke has won 12 of the 14 meetings...Thomas finished with seven points for Miami, while Plumlee had four for Duke...The Hurricanes owned a 31-29 edge on the glass.