Elizabeth Williams added 12 points and 13 rebounds for the Blue Devils.
Nikki Dixon had 17 points to lead the Tigers.
"I would say for 30 minutes we gave good effort," Clemson coach Itoro Coleman said. "But Duke did what they're supposed to do. They turned up their defense, they turned up their offense and we just didn't have enough to finish the game."
Liston finished a point from her career scoring best. She made four of Duke's five 3-pointers and rescued the Blue Devils on a poor shooting night. Duke's defense, though, helped turn the tide and forced 31 turnovers off 21 steals. Chelsea Gray had a career-high nine steals for the Blue Devils.
Duke was counting on a strong bounce back at Clemson, a team it had beaten 82-45 two weeks ago at Cameron Indoor Stadium. Instead, the bad shooting and mistakes that cost the Blue Devils in their last game surfaced again at Littlejohn Coliseum.
Duke committed 17 turnovers in the opening half — it had just 15 all game against Connecticut — and shot a dismal 31 percent (9 of 29) from the field. The Blue Devils were ahead 21-14 after Williams' inside shot with 5:56 to go before the break, then did not make another field goal the rest of the period.
The Blue Devils' starters combined for just five field goals. Alexis Jones and Chelsea Gray combined for nine of the team's turnovers. Williams, fifth in ACC scoring, was held to five points in the opening half.
Duke's defense kept Clemson from taking advantage, although the Lady Tigers scratched out an 8-1 run at the end to tie things at 22-all when Aisha Turner banked home a jumper at the buzzer.