The Heat had pulled to within 91-89 in the final minute on a Ray Allen 3-pointer, but Burke connected on a jumper from the left wing with 24.9 seconds left to seal Utah's upset win.
Burke finished with 13 points and Richard Jefferson netted 14 as the Jazz snapped a four-game losing streak
Dwyane Wade scored 19 points for Miami, which dropped a third straight in Utah.
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