The two connected for scores from 10, 43, and 35 yards as coach Bobby Hauck won his first game with UNLV (1-3, 1-1 Mountain West).
Clayton finished 14 of 20 with 194 yards passing, while Johnson had 138 yards on eight catches as the Rebels scored 45 straight points after trailing New Mexico (0-4, 0-2) by a touchdown in the first quarter.
Tarean Austin, New Mexico's first true freshman starting quarterback since 1988, finished 17 of 40 for 177 yards with a touchdown and two interceptions.
Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.
An officiating error led to an Oklahoma State touchdown Saturday in the Cowboys' 36-34 win over Kansas State.
Texas A&M receiver Ricky Seals-Jones, who was ejected for targeting midway in the second quarter of Saturday's game, took to Twitter late in the game, retweeting a tweet that questioned the call.
Florida State running back Dalvin Cook exited in the first quarter of the Seminoles' 24-16 win over Wake Forest with a left hamstring injury. He is day-to-day.
As if things weren't going bad enough at Texas, the Longhorns appear to have players on Twitter during lopsided losses and jabs at their coach accidentally being sent from other nearby teams.