Nevada (5-3) trailed 65-60 with 34 seconds remaining in regulation.
Malik Story, who finished with 13 points, hit a 3-pointer with 16.4 seconds left and, after a Washington free throw, Burton made his shot behind the arc with 4.3 seconds to go.
Terrence Ross, who led Washington (4-2) with 18 points, scored the first four points in overtime before Burton registered a three-point play and hit a 3-pointer to put the Wolf Pack ahead 72-70 with 1:39 left.
Nevada led 74-71 with 45 seconds left when Ross cut the lead to a point with a short jumper.
Burton fed Kevin Panzer for a baseline jumper with 18.9 seconds remaining to seal the win.
Olek Czyz had 10 points for Nevada.
Tony Wroten and C.J. Wilcox had 14 each for the Huskies.
Huskies dumped in overtime
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