Iowa State (2-2), which lost its 13th straight road game, scored first in overtime on a 37-yard field by Grant Mahoney for the Cyclones' first lead.
The Rebels needed one play to win it.
Clayton, who finished with three touchdown passes and one touchdown run, threw a perfect fad pass to Payne in the corner of the end zone. The same play helped the Rebels force overtime last week in their 23-20 upset of Arizona State.
UNLV (3-1) surrendered a 21-point second-half lead as Iowa State quarterback Austen Arnaud accounted for four touchdowns. The last was a 28-yard scoring strike to R.J. Sumrall with 3 seconds to play to force overtime.
The victory was UNLV's third of the season, which surpasses its win total of two in each of the past four seasons.
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Joey Counts scored on a 1-yard run on fourth-and-goal with 2 seconds left to give Montana a 38-35 victory over four-time defending FCS champion North Dakota State on Saturday.
Transfer Vernon Adams will be the starting quarterback when Oregon begins its season against Eastern Washington on Sept. 5.
Tim Beckman is threatening legal action after Illinois fired him as football coach Friday amid allegations of influencing medical decisions and pressuring players to play hurt.
LSU offensive coordinator Cam Cameron revealed in a post-practice news conference that he has been treated for prostate cancer but plans to coach this season.
The woman who accused former Baylor defensive end Sam Ukwuachu of raping her in 2013 has hired a Title IX law firm to represent her in potential civil litigation.
Arkansas tight end C.J. O'Grady has been arrested by Fayetteville police and charged with driving while intoxicated and being a minor in possession of alcohol.