Roberts hit a jump shot with 2 seconds left in the opening period that gave USC a 39-25 advantage at the break. He scored 12 of his 19 points in the first half, during which the Trojans turned the ball over just twice while holding the Rebels to 31 percent shooting from the field.
USC, with Kevin O'Neill in is first season as head coach, improved to 8-4 and won for the sixth straight time.
UNLV (12-2) had a five-game losing streak snapped. The Rebels only other loss came Dec. 12 against Kansas State.
Dwight Lewis added 14 points for the Trojans and Mike Gerrity had 13.
UNLV was paced by Oscar Bellfield with 17.