Princeton used a 12-0 run early in the first half to take a 14-6 lead on a pair of free throws by Will Venable with 8:46 left. But the Longhorns went to a half-court zone trap to force a quick tempo and trailed by just three at halftime.
Texas started the second half strong and Mouton gave the Longhorns the lead for good, 30-29, with a layup with 17:31 left. He added a three-pointer for a four-point advantage.
Brian Boddicker contributed 14 points for Texas (24-7) -- a Final Four team last year.
"Our defense kept us right there," Texas Coach Rick Barnes said. "It was terrific throughout the game."
Venable had 16 points and seven rebounds for Princeton (20-8), which had its nine-game winning streak stopped.
Texas will face North Carolina in the second round.