Montrezl Harrell led the Louisville comeback with 14 of his 22 points in the second half and 15 rebounds.
Marcus Paige scored 15 points for North Carolina (17-4, 7-2), one of four Tar Heels in double figures.
North Carolina led 43-25 with 17:51 remaining but Louisville clawed back to single digits by forcing eight turnovers in a six-minute stretch.
The Cardinals tied the game at 53 with 8:20 remaining after a 9-0 run in 80 seconds that featured 3s from Rozier and Chris Jones and a 3-point play from Harrell.
North Carolina led 59-55 with 7:10 remaining but scored just one point the rest of regulation, going scoreless for the final 3:34. Harrell's two free throws and baby hook in the lane with 3:54 left tied the game at 59. Tied at 60, Harrell hit the back iron on his open-look 3 as the buzzer sounded to send the game to overtime.
Chris Jones scored seven of his 17 points in the extra period for Louisville. J.P. Tokoto added 11 points and 11 rebounds for UNC but committed six of the team's 19 turnovers.
North Carolina had a 27-16 rebounding edge, scoring 11 second-chance points, and led 36-25 at halftime. They stretched their lead to 18 in scoring the first seven points of the second half. UNC did not get a second-chance point in the second half or overtime as Louisville used 15 offensive rebounds in that span to outrebound the Tar Heels 46-44.
Louisville hit its first two 3s of the game - appearing to have the touch it showed in shooting a combined 62 percent its last two games - but the Cardinals quickly went cold. They hit just seven of 27 shots in the half (26 percent) and went more than nine minutes without a field goal after Harrell's dunk at the 16-minute mark gave Louisville a 10-7 lead.
Louisville shot 34 percent (22 of 65) for the game compared to North Carolina's 43 percent (26 of 60).
Louisville: The comeback gave Rick Pitino his first win in seven tries against North Carolina. Three of his previous six tries came while at Kentucky, including a 1995 loss that sent the Tar Heels to the Final Four.
North Carolina: The loss ends a six-game winning streak that started three weeks ago against Louisville. Paige's layup with 8.5 seconds left capped a 13-point comeback victory that saw the Tar Heels lead for a total of 85 seconds in the second half.
North Carolina hosts No. 2 Virginia on Monday.