Darius Perkins and David Collette had 17 apiece for the Aggies (17-10, 10-5 Mountain West Conference) and Jalen Moore added 16.
Dwayne Morgan and Patrick McCaw had 13 each for the Rebels (15-13, 6-9 MWC) and Christian Wood chipped in 11 and a game-high nine rebounds.
Trailing 38-35 at halftime, USU went on an 11-2 run to start the second half behind five consecutive points from Smith and a pair of layups by Collette. The Aggies took a 55-44 lead with 11:57 to play before UNLV had an 8-0 run of their own to close the gap to 55-53.
USU answered with two quick baskets by Collette and was able to hold off the Rebels down the stretch, aided by 6-of-8 shooting from 3-point range.