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.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.