Bryce Dejean-Jones and Roscoe Smith scored 22 and 18 points, respectively, off the bench, with Smith adding 13 boards for the fourth-seeded Rebels (20-12), who will face eighth-ranked and top-seeded San Diego State on Friday in the semifinals.
Deville Smith was the lone UNLV starter to reach double digits with 15 points, shooting 3-for-5 from beyond the arc.
Josh Adams had a game-high 24 points and grabbed seven boards for the fifth- seeded Cowboys (18-14), who lost five of their last six. Jerron Granberry and Nathan Sobey netted 18 points apiece, while the latter brought down seven rebounds.
With three minutes left to play, Granberry nailed a trey to spark a 14-4 burst by Wyoming, which Sobey capped off with a three of his own that cut the margin to 65-62.
After the Rebels' Jelan Kendrick split a pair from the line, Granberry converted a 3-point play with 23 seconds left on the clock to bring Wyoming within one, 66-65.
The Rebels connected on 5-of-6 from the foul line to put the game away, however, and Sobey missed a pair from the line and two 3-point tries -- one of which was a prayer as time expired -- over the final 17 seconds.