Hickson grabbed 12 rebounds and Anthony Parker connected on four 3-pointers en route to 20 points for Cleveland, which won despite a triple-double from former Cavalier LeBron James.
Miami used three of Mike Bibby's seven 3-pointers to forge an 83-83 tie with 7 minutes left but the Cavaliers scored the next 12 points -- six of which came from Parker -- and went on to secure their first win in four games this season against the Heat.
James, making his second trip to Cleveland since leaving the Cavs as a free agent during the off-season, scored 27 points, grabbed 10 rebounds and distributed 12 assists.
Dwyane Wade fired in 24 points and Bibby finished with 23 for the Heat, who fell 2 1/2 games behind Chicago in the race for the East's top seed.
Celebrity Families of 2014 [PHOTOS]