The Wolf Pack (10-9, 5-1 Mountain West) went on a 9-0 run to open the second overtime to win.
Nevada's Jerry Evans Jr. added 15 points and AJ West had career highs of 13 rebounds and eight blocks. Huff's previous high was 16 points, Burton's 31.
Fresno State (8-12, 1-6) was 3-0 in overtime games this season before Wednesday's loss. It has now lost four consecutive games. Tyler Johnson scored 20 points and Marvelle Harris 18 to lead six Bulldogs in double figures.
Huff's layup with less than a second left sent the game into a second overtime. Burton's layup with 8 seconds left in regulation triggered the first OT.
It was the third overtime game in four meetings with the road team winning each time.
It's about time for someone other than Duke and Kentucky to grab the top class. Could it be Tom Izzo and Michigan State in 2017?
There's nowhere to go but up for the Eagles, who were winless in the ACC last season but return a slew of young players who gained valuable experience.
Officials: North Carolina must show proof of discrimination-free zone, or lose NCAA tournament games
North Carolina must prove to the NCAA that its host arenas will provide a discrimination-free zone or risk losing NCAA tournament games in 2017 and 2018, multiple officials told ESPN.