Smith had 22 points, seven rebounds and four assists to lead the fifth-ranked Blue Devils to a 56-41 victory Wednesday night.
The Blue Devils (24-2, 11-1) won their fifth straight overall, despite getting only two points from second-leading scorer Kyle Singler and being held to their lowest scoring output of the season.
"You know, points were hard to come by," Duke coach Mike Krzyzewski said. "Their defense was good. I thought ours was a little bit better.
"Again, Nolan was a huge difference in the game. To get 22 points in a game like this is a lot of points. It's a lot of points."
Singler was in foul trouble for much of the game and didn't score his first bucket until the 16-minute mark of the second half.
Krzyzewski lauded the defensive performance of sophomore big man Ryan Kelly, who also chipped in with 11 points.
"They started the four perimeter guys and could really shoot the 3, and we had to have one of our big guys guard (Joe) Harris," he said. "And Ryan was on him most of the time, and I thought did a really, really nice job because he's a very good player, and our defense of the 3 was good."
Virginia was 3 of 12 from behind the arc and Mustapha Farrakhan led the Cavaliers with 11 points.
Duke took command early in the second half, building on an eight-point halftime lead by holding Virginia to one field goal over the first eight minutes.
The Blue Devils' Mason Plumlee drew an offensive foul on Harris on one end, then dunked on the other to put Duke up 41-30.
Duke held Virginia to 15 second-half points.
Virginia (12-13, 3-8), which dropped under .500 for the first time this season, has lost three straight.
"I'm frustrated because I feel like we're better than this," Virginia coach Tony Bennett said. "Let's call it what it is — you got to be able to make some baskets and hit some shots.
"I thought there was a large stretch in the second half where we got some pretty good looks and the ball just wouldn't go in. You can't be in a game if you're shooting that percentage and struggling offensively like that."
The teams combined for seven turnovers before the first television timeout and Virginia took a 12-7 lead on Farrakhan's fast-break layup.
Duke answered with a 15-5 run over the next six minutes.
Just before the half, Smith raced out in transition and converted a layup as he was being fouled by Sammy Zeglinski. While standing over Zeglinski, Smith did a little dance.
Duke was in control the rest of the way.
The Blue Devils led 34-26 lead at the break and clamped down on the Cavaliers in the second half.