The Blue Devils (22-2, 9-1 ACC) fell to new league rival Notre Dame 88-67 last Sunday and trailed Clemson (11-13, 3-7) late in the first half of this one. But Duke put together a 32-12 run starting in the final minute before halftime to take control.
It was Peters' first double-figure showing in three games while Liston posted her third game this season with double figures in points and rebounds.
The Blue Devils held Clemson's top scorer, Nikki Dixon, to 10 points on 3-of-12 shooting. Dixon had been averaging better than 14 points a game this season.
Richa Jackson had 13 points and Ka'lia Johnson added 10 for Duke.
Duke needed a soft place to land after its disappointing loss to No. 2 Notre Dame on Sunday and Clemson has generally been just that for the Blue Devils, all but one of whose 18 straight series wins have come by 14 points or more.
A year ago, Duke was coming off a defeat to top-ranked Connecticut and rebounded with a 60-46 victory at Littlejohn over the Tigers.
And this one started out like many of the others with Duke in charge.
Blue Devils coach Joanne P. McCallie groused about her team's lack of stops in the Notre Dame loss. There wasn't a similar drop off this time as the Tigers were held to 1-of-12 shooting the first eight minutes and Duke jumped out to an 11-2 lead.
Things changed dramatically after that as Clemson found its shooting touch and Duke struggled to hold on to the ball.
The Tigers took off on a 16-6 run to take an 18-17 lead on Dixon's steal and layup with 4:35 to go. Ka'lia Johnson came back moments later with basket in traffic and got fouled for a three-point play to retake the lead.
Clemson moved back on top on Nyilah Jamison-Myers inside basket, 23-22, with 1:17 left. That's when Duke turned things up to score three baskets in the final minute.
Alexis Jones started it with a straight-on jumper, Johnson drove the lane for bucket and Williams pulled off a reverse with 2.6 seconds to send the Blue Devils into the break ahead 28-23.
Not that McCallie didn't have plenty to shore up in the second half.
Duke, which had just 16 turnovers against Notre Dame, had 15 in the opening 20 minutes Thursday night. The Blue Devils are averaging 17 turnovers a game this season.
Whatever she said worked as her team tightened up and turned the ball over just six times in the second half.
While Williams' ACC-record streak of 91 games with a block came to an end in the loss to the Fighting Irish, she started a new one with two of Duke's four blocks against Clemson.
Duke also shot the ball well at 57.1 percent. The Blue Devils had 17 field goals in the second half, the same amount as Clemson had all game.
The Blue Devils will have to wait a game for the chance to restart another ACC streak that Notre Dame ended—they had won 42 straight league games at Cameron Indoor Stadium. They face rival North Carolina there Monday night.