Brittney Martin added 13 points and her free throw with 7:50 left put the Cowgirls up 51-45.
That's when Duke finally started playing like a No. 2 seed going for its 18th straight NCAA tournament victory at home.
Alexis Jones hit a free throw before Liston finally warmed up after a 2-for-12 start, scoring six straight points to give Duke its first lead since the opening minutes.
She stuck back her missed jumper, drew contact, hit the following free throw and then buried a 3-pointer with 5½ minutes left to put the Blue Devils up 52-51.
That got Duke's decisive 17-2 run rolling, scoring on five straight possessions with Jones' free throws maxing out the lead at 62-53 with 53.8 seconds left.
By that point, their 15-point hole — their largest deficit at Cameron all season — was a distant memory.
They fell that far behind in the first minute of the second half and were in danger of being run completely off their home court before they got back in it with 12 straight points.
"You can want things too much sometimes and press a little bit and forget to play together," McCallie said. "Second half, very different story. Everybody on the same page, everybody pulling in the same direction and I thought it was a fascinating thing to be a part of."
That came after a first half in which the Cowgirls came into Cameron and made themselves right at home.
They led for all but about 2 minutes of the half while shooting nearly 47 percent in the opening 20 minutes.
Toni Young finished with 12 points and Tiffany Bias added 11 for Oklahoma State, which held Duke to 18 percent shooting from 3-point range in the first half.
"We're a fast and quick team, and we used what we got to build a lead against them," Young said.