Three days after defeating then No. 1 North Carolina, the unbeaten Rebels barely survived in a game they led by eight points with less than 2 minutes left in regulation.
Both Marshall and Stanback scored four points in the second overtime and both hit a pair of free throws in the final 40 seconds.
The Rebels improved to 8-0 and the Gauchos slipped to 4-2.
California-Santa Barbara tied the game with a second left in regulation when Orlando Johnson intentionally missed a second free throw attempt and Greg Somogyi made a layup after grabbing the offensive rebound.
With 13 seconds left in the first overtime and the game still tied, Stanback fouled James Nunnally as he attempted a 3-point shot. Nunnally made all three free throws for the Gauchos, giving them an 84-81 lead.
Stanback then grabbed the rebound of a missed 3-point try by Marshall and hit his 3-point attempt to again tie the contest.
Marshall missed two free throws and also missed a layup in the second extra period, but his two free throws with 40 seconds left put the Rebels in front by six.
Mike Moser made 12-of-18 shots and scored 34 points to leave UNLV.
Johnson scored 36 points for California-Santa Barbara.