Clayton, who threw for a career high 340 yards, found Payne on the right side of the end zone with an up-for-grabs pass capping a 14-play 67-yard drive for the Rebels (2-1).
UNLV beat the Warriors (2-1) despite the efforts of Greg Alexander, who completed 31 of 48 passes for a career high 477 yards and three touchdowns. Alexander's final desperation pass was batted down by UNLV wide receiver Ryan Wolfe as time expired.
Wolfe finished with 130 yards receiving and Payne added 94.
Clayton was 28-of-43 with two interceptions.
The Warriors had taken the lead with 5:27 left on Alex Green's 2-yard touchdown run.