''Whatever reservoir we had there at the end, we were able to get through,'' Duke coach Mike Krzyzewski said. ''This team has a really good will to win. You have some shortcomings, which all teams do, but at the end of the day, they have a will to win.''
Miles Plumlee added 15 rebounds and two free throws with 9.6 seconds left for the Blue Devils (25-4, 12-2).
Less than 48 hours after claiming a critical victory at No. 15 Florida State, they found a way to win their sixth straight and remain atop the league standings with a week left in the regular season - which ends with their rivalry rematch with No. 7 North Carolina.
''You're fighting human nature,'' Duke forward Ryan Kelly said. ''You just got a huge victory on the road, you're just tired and fatigued. We need to get rejuvenated for next week because it's going to be a huge week.''
Duke essentially won this one at the free throw line. The Blue Devils made 24 of their 34 free throws, including 6 of 8 in the final minute of overtime. The Hokies - who entered making an ACC-best 73 percent of their foul shots - were 7 of 16.
''Part of the game,'' said Virginia Tech coach Seth Greenberg, his voice reduced to a near-whisper. ''Players miss free throws. It's not just our team. All teams.''
Dorenzo Hudson, one of three players with 16 points for the Hokies (15-14, 4-10), pulled them to 64-63 with a deep jumper with 1:19 left in OT.
Mason Plumlee's free throw with 51.1 seconds left made it a two-point game, then had a hand in Hudson's face during his jumper that would have tied it.
After Rivers' free throw with 19.4 seconds left made it 66-63, Erick Green missed a layup and Miles Plumlee's free throws extended Duke's lead to five. Green hit a layup with 2.9 seconds left before Curry hit two free throws with 0.2 seconds to play.
Green and Cadarian Raines also scored 16 points apiece for the Hokies. All of Green's points came after halftime, giving him an ACC-best 30th straight double-figure game.
Virginia Tech had the last chance to win it in regulation, with the ball with 32 seconds left. Green dribbled out much of the clock before his 15-footer bounced off the rim with about 5 seconds left. Raines then soared in from the left side for the rebound but tossed it off the side of the rim before the buzzer sounded.
''I thought we did a lot of good things. We competed at a very high level,'' Greenberg said. ''We just weren't able to finish.''
That came after Hudson banked in a 3-pointer over Curry to make it 58-55 with 1:26 left. Mason Plumlee pulled Duke within one point with a stickback with 48 seconds left, and Rivers made one of two free throws with 32 seconds left to tie it.
''You try to go up there and at worst get to overtime, and the best is obviously not to go into overtime,'' said Rivers, who faced the same situation in Duke's overtime loss to Miami earlier this month - making one free throw when two would have given his team the lead.
Duke used its disparity in free throws to overcome 38.5 percent shooting and a 6-of-24 performance from 3-point range; they had made at least eight 3s in each of their previous seven games. The Blue Devils also built a 44-38 rebounding advantage to improve to 16-1 against the Hokies at Cameron Indoor Stadium.
Dorian Finney-Smith added 15 rebounds for the Hokies, who have lost two straight and seven of 10. Their previous four games were decided by a total of five points, most recently a two-point home loss to rival Virginia.
With actor Rob Lowe watching from the front row behind the scorer's table, the Blue Devils never led by more than seven points.
Curry - whose father Dell was one of the best players in Virginia Tech history in the 1980s - scored seven points during a 9-0 run that gave Duke a 46-40 lead midway through the second half. The Hokies countered with a 9-2 spurt and went up 49-48 on Green's jumper with just under 6 minutes left. After that, neither team led by more than three until midway through overtime.
''We fought hard,'' Green said. ''We played a good 45 minutes instead of one half.''