The Tar Heels overcame a 12-point deficit in the second half to tie it with 2:14 to go, but Texas made the key plays down the stretch to win its sixth in a row.
Texas had a one-point lead when Holland went to the foul line with seven seconds remaining. He missed both attempts, but dashed down the lane to grab the rebound on his second miss. Holland followed that with a layup that accounted for the final score.
Marcus Paige missed a 3-point try for the Tar Heels at the buzzer.
Texas (10-1) outrebounded North Carolina 51-37 to help overcome the Tar Heels' constant but often unsuccessful parade to the foul line. North Carolina went 24-of-47 from the charity stripe and the Tar Heels would have finished below 50 percent had Paige not made all eight of his attempts.
Isaiah Taylor led Texas with 16 points, Jonathan Holmes had 15 and Holland added 13.
Paige paced the Tar Heels (7-3) with 23 points and eight rebounds.