The Golden Bears became the second No. 12 seed from the Pacific-12 Conference to escape with a victory Thursday and moved on to meet Syracuse, which demolished Montana 81-34. The Oregon Ducks also won as a No. 12 seed when they defeated Oklahoma State earlier in the day.
California led by nine with 6 minutes to play, but the Rebels closed within one when Anthony Marshall hit two free throws with 6 seconds left.
Crabbe then made two foul shots with 2 seconds to go for what turned out to be the final margin.
California stole the inbound pass after Crabbe's free throws and Richard Solomon was fouled. He missed both foul shots, however, giving UNLV at least a chance at a desperation 3-point heave.
That attempt by Anthony Bennett missed, however, and the Rebels were eliminated in their opening tournament game for the fourth straight season.
Justin Cobbs added 13 points for California (21-11), which went just 4-of-12 from the line in the closing minute.
Bennett scored 15 points and had 11 rebounds to lead UNLV (25-10).