The Heat rallied from an 18-point deficit in the third quarter but wasted the comeback in a setback that ended their nine-game winning streak. Utah has won two in a row after losing six out of seven.
Dwyane Wade drew Miami even by making 1-of-2 free throws with 14 seconds remaining. Wade, however, committed a foul as Harris was making a floating jump shot and the resulting free throw forced the Heat to try a 3-pointer.
Udonis Haslem missed that try at the buzzer.
LeBron James scored 35 points for Miami and had 10 rebounds and six assists.