In a strange game that saw both teams lose their starting quarterbacks, the Wolf Pack tied the game in the final seconds of regulation as Combs connected with Richie Turner from 44 yards out to tie the score at 28.
Nevada (5-1, 2-0 Mountain West) led 21-7 in the second quarter when starting quarterback Cody Fajardo went down with back spasms with 5:04 left to play. He did not return.
Nevada coach Chris Ault praised Combs, a sophomore who finished 11 of 19 for 217 yards and two touchdowns.
"It took Devin some time to find himself, but he did and I'm proud of him," Ault said. "To bring this team back in the fourth quarter and then win this thing, that was pretty special."
Fajardo was 19 of 26 for 221 yards and two touchdowns and an interception. His 20-yard scoring pass to Kendall Brock put Nevada ahead 21-7 with 9:50 left in the first half.
Wyoming (1-4, 0-1) came back behind quarterback Brett Smith, who was ejected with 8:16 left in the fourth quarter after receiving a second unsportsmanlike conduct penalty.
Smith's 8-yard touchdown run with 13:07 left in the game had given the Cowboys a 28-21 lead. He received his first unsportsmanlike penalty after the touchdown for taunting.
The second came on the Cowboys' next drive when Smith protested a Nevada defensive holding penalty that was waved off by the officials.
Wyoming coach Dave Christensen was critical of the call.
"Guy's running off the field, 3 yards from the sidelines running off the field, takes his helmet off and you're going to throw a flag on him," Christensen said. "Kick him out of the game? That's unbelievable."
Smith was 21 of 34 for 197 yards and three touchdowns. His replacement, Jason Thompson, was 1 of 6 for 10 yards.
Nevada had the ball first in overtime, starting at the 25. After rushing for 1 yard on the first play, Combs hit Bradley cutting across the middle from 24 yards out.
Wyoming then took over at the 25 and after Thompson rushed for 1 yard on the first play, he threw three consecutive incomplete passes to end the game.
The Cowboys held Wolf Pack running back Stefphon Jefferson, the nation's leading rusher entering the game, to 78 yards on 23 carries, nearly 100 yards fewer than his season average of 174.
"I think our guys did a nice job stepping up against the run, but gave up far too many passing yards," Christensen said."
Welcome to the Thanksgiving edition of the Pac-12 mailbag, which includes playoff talk and analysis of Rich Rodriguez's future.
After months of cheering for your team to win, its time to extend that goodwill to others. Heather Dinich breaks down who you need to cheer for if you want your team to make it in to the College Football Playoff.
Texas A&M head coach Kevin Sumlin joins David Greene on SEC Film Room to analyze the Aggies' win against Vanderbilt.
ESPN College Football reporter Chris Low discusses why Kirby Smart is emerging as a top candidate for the South Carolina head coaching position.
What we're thankful for in the Pac-12 this season, including an influx of young talent, surprises both good and bad, and the College Football Playoff.
Clemson defensive coordinator Brent Venables and Alabama defensive coordinator Kirby Smart are among the 34 nominees for this year's Broyles Award.