Jon Scheyer missed his first nine shots and Nolan Smith missed his first six for the Blue Devils, who shot 31 percent in the opening half to fall behind 37-25. But 22 turnovers doomed the Hurricanes, who attempted only 45 shots to 60 for the Blue Devils.
Duke outscored Miami 29-9 to start the second half and shot 9 for 15 from 3-point range after halftime.
The Blue Devils (22-4, 10-2 Atlantic Coast Conference) increased their league lead with their fifth win in a row. Miami (17-9, 3-9) lost for only the second time in 13 home games.
Despite their poor starts, Smith finished with 21 points for Duke, and Scheyer scored 15 despite shooting 3 for 15. Dwayne Collins had 21 points and nine rebounds for Miami, and Durand Scott scored 19 points.
Scheyer was 1 for 12 before sinking 3-pointers on consecutive possessions for a 64-59 lead with five minutes left. Smith's 3-pointer capped an 8-0 run that put the Blue Devils up 69-59, and the margin was at least five the rest of the way.
Duke went 9 for 10 from the free-throw line in the final 90 seconds to seal the win. The Blue Devils scored 56 points in the second half — remarkable considering that in the first 12 minutes, they shot 4 for 19 with seven turnovers and fell behind 23-12.
Smith was shut out for the first 18½ minutes. Scheyer struggled even longer, finally scoring 24 minutes into the game to pull Duke even at 39.
Duke missed nine of its first 11 shots, and Miami scored 11 consecutive points — eight by Collins — for a 15-6 lead. Scott sank a runner at the buzzer to end the half to put the Hurricanes up 37-25, their largest lead of the game.
Singler made four baskets in the first 2½ minutes of the second half to trim it to five, and his 3-pointer gave the Blue Devils their first lead since the early minutes at 42-41.
On next possession, Smith's 3-pointer put Duke ahead to stay.
The Hurricanes were outscored by 27 points from 3-point range, and the loss ensured they'll finish below .500 in the league. They've never been better than 8-8 in the ACC.