The Badgers held a 2-0 lead following a first half goal off a free kick by sophomore forward Bryce Privett from Bayside Academy in Fairhope, Ala., and a goal in the 63rd minute by freshman team captain Andy Poveda of Niceville, Fla., off an assist by Privett.
GSW, however, stormed back to tie the match with late goals in the 73rd and 88th minutes, forcing a ten-minute overtime period.
As the clocked ticked down in overtime, Burns headed a Privett corner kick into the goal with just one second showing on the scoreboard for the game-winner.
Corey Bronenkamp of St. Louis, Mo., picked up the win in goal with five saves.