Quinn Cook scored 15 points and Mason Plumlee scored eight of his 10 in the second half for the Blue Devils (13-0), who are one of only four undefeated teams remaining in Division I. Tyler Thornton added 10 points, including a pair of 3-pointers in the second half to spark Duke.
"For our guys to go 13-0 with our nonconference schedule is just magnificent," Duke coach Mike Krzyzewski said. "It's terrific."
The game was tied 29-all at halftime before Duke opened the second half with a 12-0 run. The Blue Devils, who led by as many as 19 in the second half, heated up from 3-point range after the break, going 3 for 4 in the early minutes of the period.
During that six-minute span to open the second half, the Wildcats had nine empty possessions.
"That's when they made their run," Davidson coach Bob McKillop said. "You wipe that six minutes out, well. ... But that's why Duke is number one. Somehow they are going to make you pay during that six-minute period. They've done that in every game they played this year."
Curry, playing in front of his hometown fans and against his older brother Stephen's alma mater, had a rough night, finishing with six points on 3-of-11 shooting. Earlier in the day, Stephen Curry -- who plays for the Golden State Warriors -- wrote on Twitter that he was rooting for Davidson but hoping his brother dropped 30-plus points.
That didn't happen, but Kelly picked up the slack, hitting 5 of 8 from the field -- including 3 for 4 from 3-point range.
"I got the shots that I wanted. I just wasn't able to get them to go down," Curry said. "Maybe I was pressing a little early trying to get going. I'm just going to have to bounce back on Saturday."
It didn't help that Davidson placed an emphasis on rotating and taking away opportunities from Curry and Plumlee.
That benefited Kelly, who was left open for shots.
"They were physical, they were riding us," Kelly said. "That made it tough on Mason to get his shots. But once we figured it out, we saw the holes in it. Mason is the type of player where he's unselfish. He passed out of double teams and it created for others."
Duke is set to open ACC play at home against Wake Forest on Saturday, while Davidson is home to face Southern Conference foe UNC-Greensboro.
Jake Cohen led Davidson (7-6) with 19 points and eight rebounds despite battling through early foul trouble, and De'Mon Brooks pulled down 12 rebounds and scored eight points in the Wildcats' 24th straight loss to Duke.
Plumlee scored on an inbound play to ignite Duke's 12-0 burst coming out of halftime.
Kelly followed with a pair of free throws, Cook hit a foul-line jumper and Thornton knocked down a 3-pointer from the wing. Kelly capped the run with a 3-pointer from the left corner, his third of the game, to push the lead to 12.
Duke had seven assists and two turnovers in the second half after just one assist and nine turnovers in the first 20 minutes.
They held Davidson to 30 percent shooting for the game, and the Wildcats were just 4 of 19 from behind the arc.
"I thought our defense was terrific," Krzyzewski said.
Davidson, which hung tough in the opening half, would never get closer than eight after Duke's run to start the second half.
The Wildcats entered the locker room at halftime tied despite shooting just 32 percent in the first half. Cohen, last year's co-conference player of the year along with Brooks, sat out 15 minutes after picking up his second foul less than three minutes in.
Davidson did it with hustle, outrebounding the taller Blue Devils 22-15 in the opening half, including a 9-1 edge on the offensive boards.
"In the first half we gave up offensive rebounds and in the second half we didn't and to me that was the key to the ball game," Krzyzewski said.
Brooks, who has been a factor inside for the Wildcats all season, struggled to get off shots against Duke's defenders, who began collapsing on him in the paint. He finished 4 of 13 from the field.