Johnson's two free throws broke a 60-all tie and helped the second-seeded Blue Devils (27-5) avoid a three-game sweep by their fiercest rival. Duke went made all six of its free throws in the final minute of a tight game, holding off UNC freshman star Diamond DeShields and the sixth-seeded Tar Heels (24-9).
After Oderah Chidom hit two more free throws to make it 64-61 with 17.5 seconds left, DeShields launched a 3-pointer for the tie but it rattled out.
Liston made just two shots after halftime, but the second was a huge 3-pointer at the 2:02 mark to cut the Tar Heels' lead to 59-58. Then, after Xylina McDaniel's free throw, Elizabeth Williams scored on a stickback to tie the game at 60 with 1:18 left.
DeShields scored 25 points and hit five 3-pointers to lead the Tar Heels, with four of those coming after halftime. But she committed a technical foul for taunting Haley Peters after hitting a jaw-dropping step-back 3 with 8:08 left, one of a series of small mistakes that proved costly when Duke pushed ahead late.
UNC went just 2 for 7 at the foul line in the final 6:14, including reserve N'Dea Bryant making 1 of 2 after being fouled on a jumper after Johnson's big free throws. The Tar Heels also somehow managed to have the wrong people taking shots at key moments, with Latifah Coleman missing a driving basket as the shot clock wound down in a tie game and Bryant being bailed out on her quick jumper by drawing Williams' fifth foul.
Williams finished with 12 points, nine rebounds and three blocks, including a big one on Stephanie Mavunga's stickback attempt on Coleman's missed drive. Mavunga fouled Johnson on the scramble for the rebound to set up the go-ahead free throws.
The Tar Heels won the first meeting in Duke's Cameron Indoor Stadium 89-78, earning their first win in the building since 2008. DeShields went for 30 points in that game, then went for 18 in last weekend's 64-60 home win to close the regular season.
North Carolina was poised to add another win against Duke, with DeShields knocking down three 3s and fellow freshman Allisha Gray one of her own to break a 31-all halftime tie and give UNC a 43-35 lead with 16:42 left.
Gray finished with 14 points and seven rebounds for the Tar Heels, who shot 34 percent and went 9 for 30 from 3-point range.
Follow Aaron Beard on Twitter at http://www.twitter.com/aaronbeardap