Colorado State (7-6) trailed most of the game before taking the lead on Wyatt Bryan's 38-yard field goal with just under 4 minutes left.
The Wolf Pack (7-6) responded quickly, marching 72 yards in eight plays to set up Butler's tackle-breaking touchdown run.
Nick Stevens orchestrated a quick-hitting drive in the final minute with no timeouts, but receiver Jordon Vaden was unable to get out of bounds at Nevada's 12-yard line and time ran out on the Rams.
Stevens ran for 189 yards and Elijah Mitchell scored on a 96-yard kickoff return in the bowl battle between Mountain West Conference teams.
Stevens threw for 310 yards and a touchdown.
Meanwhile, in Fort Worth, Jared Goff threw for 467 yards and six touchdowns and California won in the postseason for the first time in seven years, beating Air Force 55-36 in the Armed Forces Bowl on Tuesday.
Goff had three of his scoring tosses in a span of five plays in the second quarter as the Bears (8-5) broke a 14-14 tie and cruised in a rematch of the 2007 Armed Forces Bowl, also won by Cal (42-36).
Receiver Kenny Lawler had three touchdowns for Cal, which last made the postseason in a 21-10 loss to Texas in the Holiday Bowl in 2011. The Bears' last bowl win was 24-17 over Miami in the 2008 Emerald Bowl near their Bay Area campus.
Weakened by the targeting ejection of secondary anchor Weston Steelhammer on Air Force's third defensive play, the Falcons (8-6) lost for the fourth time in five Armed Forces appearances since 2007.