UNLV nursed a small lead through most of the second half, but Greene made a layup with 47 seconds left to pull Colorado State within a point at 61-60. After Matt Williams blocked a layup attempt by UNLV's Marcus Banks, the Rams got the ball to Greene, and the resilient senior forward somehow made an off-balance jumper over two defenders.
The Rebels then botched the inbounds pass, but Colorado State's Shelton Johnson missed a free throw with 2.9 seconds left, and UNVL got the rebound and called timeout.
Banks' half-court heave as time expired ricocheted high off the backboard, setting off a wild celebration at center court for the players, coaches and dozens of fans who sprinted down the stairs to dance and shout on the Rebels' court.
It was the third upset victory in three days for the Rams, who beat third-seeded Wyoming on Thursday and second-seeded BYU on Friday. Colorado State hadn't even won a game in the first three years of the Mountain West tournament, but the Rams are headed to the postseason for the first time under third-year coach Dale Layer.
Banks, a Las Vegas native playing his final home game, had 16 points and seven assists for the Rebels (21-10), who wasted a golden opportunity to clinch their first NCAA trip in three years.
Jermaine Lewis scored 14 points for the Rebels, while J.K. Edwards had 10 points and nine rebounds. After losing the tournament title game at home for the second straight year, UNLV must hope for an at-large berth, which probably won't come.
Nelson scored 17 points for the Rams, but the star sophomore was knocked out of the game with 13:06 left when he hurt his head during a scramble for a loose ball. Nelson stayed on the court for several minutes, and after sitting briefly on the bench, he walked unsteadily to the locker room and didn't return.
Colorado State didn't immediately disclose the nature of his injury, but he was healthy and smiling while accepting the MVP award after the game.