Nolan Smith added 18 points on 5-of-18 shooting for the Blue Devils (15-0, 2-0 ACC). They overcame 17 turnovers and shot 40 percent to extend their best start since 2005-06.
Jordan Williams had 23 points and 13 rebounds for his ninth straight double-double, and Cliff Tucker added 14 points for the Terrapins (10-5, 0-2). They were the last team to defeat Duke, but they were denied their 11th win against a No. 1 team in school history.
Maryland closed to 67-62 on Williams' layup with 1:25 left, but Singler responded with a 3-pointer with 53 seconds left and the Terps couldn't get closer than six after that.
Seth Curry added 12 points for Duke. The reigning national champions extended their winning streak at Cameron Indoor Stadium to 29, have defeated 51 consecutive unranked opponents on their home floor and have won four in a row over Maryland at home.
Smith, the ACC's leading scorer, had his streak of 20-point games snapped at five and was afforded few easy opportunities by a Maryland defense determined to slow him down.
That seemed to open things up for Singler, who was 10 of 19 from the field. After the Terps closed to 55-54 with 6 1/2 minutes left, Singler hit a 3 to start an 8-2 spurt. He closed it with a layup that made it 63-56 with 4:20 left, and Maryland couldn't make it a one-possession game the rest of the way.
The Blue Devils trailed 38-32 one minute into the second half, but used a Curry-led 14-2 run to take a six-point lead. Curry scored nine points during the burst, capping it with a 3 from the corner that made it 46-40 with about 13 minutes left.
The Terrapins, who pulled a 79-72 upset of Duke last March in College Park, had the star of that game - Greivis Vasquez - sitting in the stands behind their bench for this one.
For a while, at least, he had to like what he saw.
Maryland kept things tight in the first half, forcing 10 turnovers - or, more than the Blue Devils committed in five games - while holding them to an uncharacteristic 1-for-10 shooting from 3-point range. Singler's tip-in just before the buzzer put Duke up 32-31, their slimmest halftime lead of the season at Cameron.
It didn't last long. The Terrapins reeled off seven quick points in the opening minute of the second half and went up by six on Sean Mosley's tip-in.