Cornett's first-quarter run was the longest rushing score for the Rebels (1-2) in 22 years.
The Warriors (1-2), which were a 20 1/2-point favorite, fumbled four times.
UNLV's Caleb Herring was 17 of 29 passing for 178 yards and two touchdowns, both to Payne.
TCU had a lot to overcome, from torrential rains to an ankle injury that slowed Trevone Boykin, but the Horned Frogs dug deep to knock off Baylor.
Check out highlights from TCU's 28-21 double-overtime win over Baylor.
In a game that was marked by inclement weather, TCU prevails for the victory over Baylor in double overtime.
SEC Nation previews the Ole Miss vs. Mississippi State matchup.
SEC Nation previews the matchup between in-state rivals Florida and Florida State.
Players and coaches from Alabama and Auburn discuss the tradition of the Iron Bowl and the 2015 matchup.