UNLV (4-6, 2-4 Mountain West) needs to beat its last two opponents, Air Force on the road and San Diego State at home, to earn bowl eligibility. Colorado State (3-7, 0-6) lost its seventh straight.
Clayton was 10-of-17 for 147 yards and no interceptions. He rushed for 44 yards on seven carries.
Clayton had a role in both of the Rebels' first-half touchdowns. He scored on a 28-yard run down the left sideline early in the second quarter, then found Jerriman Robinson for a 13-yard pass with 54 seconds remaining before halftime.
UNLV backup quarterback Mike Clausen ran for a pair of 5-yard touchdowns in the second half.
Clausen's second score was set up by Marquel Martin's interception of Colorado State backup quarterback Jon Eastman. The turnover ended a 30-quarter UNLV interception drought.
Colorado State's only TDs came on Jon Mosure's 1- and 2-yard runs.
Rams starting quarterback Grant Stucker was 13-of-24 for 127 yards and no interceptions. Rashaun Greer caught seven passes for 77 yards.
It was Colorado State's first loss at UNLV after six wins and a tie.