Sheldon McClellan banked in a putback jumper with 25.9 seconds left to put Texas within two points, but J.T. Terrell made two free throws on the next possession to seal the victory for the Trojans.
Eric Wise led USC (3-1) with 13 points. Julien Lewis had 17 for Texas (2-2).
In a game with 12 ties and nine lead changes, neither team led by more than three points after halftime until overtime.
Both teams combined to shoot under 36 percent -- under 30 percent in the second half.
USC will play Marquette on Wednesday in the tournament's fifth-place game.