Austin Rivers and Seth Curry added 11 points apiece for the Blue Devils (14-2, 2-0 Atlantic Coast Conference).
Despite an off night from 3-point range, they shot 52 percent against one of the league's stingiest defenses, put together a game-changing run shortly after halftime, then held off Virginia's late push to claim their second straight win.
Mike Scott scored 23 points for the Cavaliers (14-2, 1-1). They pulled within three on Akil Mitchell's stickback dunk with 47.6 seconds left, then forced a stop and had the ball with about 13 seconds left. But Scott missed a 3-pointer from the corner and Jontel Evans missed a 3 from the wing as time expired.
Andre Dawkins finished with 10 points for the Blue Devils. They were held 21 points below their average of 82, were just 5 of 20 from 3-point range and gave the Cavaliers a prime chance to force overtime before clinching their 19th straight ACC win at home, their 44th in a row at Cameron Indoor Stadium and their 14th consecutive win there against the Cavaliers.
Virginia hasn't won at Duke since 1995, when Hall of Fame coach Mike Krzyzewski was out due to back surgery and exhaustion.
Joe Harris added 14 points but Sammy Zeglinski, who averages 9.9 points, finished scoreless on 0-for-8 shooting for Virginia, which debuted its highest ranking since climbing to No. 15 in 2002 and had a chance to force overtime despite managing just one field goal in a 7½-minute span early in the second half.
The Cavaliers entered giving up an ACC-best average of 50.5 points, and their defense held the Blue Devils in check for a while.
But immediately after the break, it was Duke's turn to dictate tempo. Rivers started the 23-10 spurt that put Duke in charge for the first time, following up Ryan Kelly's missed jumper with a layup that cut Duke's deficit to 34-32 with just under 19 minutes left.
Plumlee scored seven points during the run, including a left-handed hook shot that gave the Blue Devils their first lead since midway through the first half and a three-point play that capped it and made it 53-42 with 9:37 left.
Meanwhile, during that stretch, the Cavaliers simply went cold.
After Scott hit a jumper with 19:15 left, Virginia hit only one of its next nine attempts before Harris' basket with 11:46 remaining. That was before Mitchell personified the Cavaliers' early second half shooting struggles when he soared for a dunk of Harris' missed 3 — and instead slammed the ball hard off the back iron.
By contrast, Virginia was in charge at both ends for much of the first half, with Scott scoring 16 points before the break.
The Cavaliers held Duke to one field goal during a stretch of more than 9 minutes midway through, and the Blue Devils missed nine of their first 11 attempts from long range. Duke's 28 points matched a season low for the first half set against Ohio State.