Andre Dawkins added 12 of his 14 points after halftime, Kyle Singler finished with 13 points and Mason Plumlee had a career-high 16 rebounds for the slow-starting Blue Devils (16-1, 3-1 Atlantic Coast Conference).
They trailed by 10 late in the first half but outscored Virginia 43-18 over the final 16 minutes and shot nearly 47 percent to avoid their first losing streak in two years.
The Blue Devils almost certainly won't have that designation much longer, after Florida State beat them 66-61 three nights earlier.
Their first defeat since Maryland knocked them off last March snapped the 25-game winning streak that included the run to the program's fourth national championship.
Still, Duke kept a few other streaks intact by winning its 30th straight game at Cameron Indoor Stadium, its fifth straight against Virginia and its 14th in a row against the Cavaliers in Durham.
And they have Dawkins to thank for much of it, after the sophomore made a series of big plays during the burst that erased a nine-point deficit and put Duke up by double digits for the first time.
First, he put the Blue Devils up to stay by knocking down a hanging jumper through contact from Harris and hitting the free throw that followed to make it 45-44 with 12:15 left.
Seconds later, he stole the ball from Harris and found Smith, who streaked the other way for a highlight-reel dunk over Akil Mitchell that sent the Cameron Crazies into delirium.
The third of Dawkins' three 3-pointers during the run stretched Duke's lead to 62-52 with just inside of 7 minutes left. Virginia didn't get closer than eight the rest of the way, and remained winless in 14 tries on a No. 1 team's home floor.
For about 24 minutes, though, Duke's 3s weren't falling -- a major reason why the ACC's top-scoring offense was being outscored by the league's worst. Duke averages more than 86 points while the Cavaliers score fewer than 64 points per game.
Some of the same problems that plagued Duke against Florida State reappeared early in this one: relying too heavily on -- and missing -- 3-pointers. The Blue Devils missed 11 of their first 12 attempts from long range, and during one 6-minute stretch, they attempted only one shot inside the arc while hoisting up seven shots from behind it. Duke finished 5 of 20 from 3-point range, 4 of 8 in the second half.
Virginia led for most of the half, reeling off eight straight points and taking a 27-17 lead on Farrakhan's 3 with 3 1/2 minutes left. The Cavaliers led 31-25 at the break -- Duke's largest halftime deficit of the season -- and twice led by nine in the second half, the last on Will Sherrill's layup with 16:13 left.