UNLV's Anthony Marshall hoisted a tough shot from the foul line that missed the basket completely as the clock wound down, but Thomas corralled the air ball between two defenders and put it in for the game-winner.
He was also fouled on the play and intentionally missed the free throw to produce a rebound. Cal nabbed it but didn't have enough time to set up for a last-ditch shot.
Anthony Bennett pumped in 25 points to go with 14 rebounds, while Bryce Dejean-Jones added 22 points for the Rebels (7-1).
The Golden Bears (6-2) were led by Allen Crabbe's 18 points.