Seth Curry added 18 points for the Blue Devils, who watched the three teams above them in the AP Top 25 lose to unranked opponents this week, and then nearly joined them.
Olivier Hanlan scored 20 points for Boston College (10-13, 2-8 ACC). The Eagles led by five points with 2:15 left and had a chance to win it after Plumlee made one of two free throws but Hanlan's jumper was wide and the rebound popped out of bounds as the buzzer sounded to end the game.
Duke (21-2, 8-2) won its fifth straight game.
The Eagles entered the day tied for last in the conference, but they jumped to an eight-point lead midway through the first half and held onto a tie at halftime. Duke quickly erased the deficit as the second half began and opened a six-point lead but then went cold again, scoring just one free throw over a 4 1/2-minute span and allowing BC to make it 61-56 with 2:15 to play.
But Quinn Cook made his third 3-pointer of the game, then Plumlee hit a pair of free throws with 47 seconds left to tie it 61-all. BC's Joe Rahon put a 3-point attempt off the top of the backboard and Plumlee was brought down hard as he grabbed the rebound.
The Blue Devils forward misses the first foul shot but made the second to make it a one-point lead.
After a timeout, Hanlan dribbled down the clock, before faking the drive and pulling up for an open shot inside the foul line that was wide. Ryan Anderson grabbed the rebound but lost control as he fell to the floor and the ball popped out of bounds as the buzzer sounded to end the game.
Plumlee celebrated from his back as the Blue Devils improved their chance to move up from the No. 4 ranking after losses for the top three teams: Indiana, Florida and Michigan, all to unranked teams. The Blue Devils have been ranked No. 1 five weeks during the regular season, the last on Jan. 21.
Fans dug themselves out after the weekend's blizzard to watch the Eagles play their best game of a season that includes losses to Harvard and Bryant. BC had lost six of seven, including a 22-point loss to No. 8 Miami on Tuesday.
Duke went scoreless for the first five minutes of the game and trailed by as many as eight points, 13-5, in the first half, and it led 21-14 before scoring 11 of the next 14 points, taking its first lead of the game on Plumlee's three-point play with 1 minute left in the first half.
It was 27-all at the half before Curry and Cook hit 3-pointers and Curry followed with a four-point play that gave Duke a 39-34 lead.