The game was marred by a serious injury suffered by Miami center Alonzo Mourning. Miami officials said Mourning, 37, tore the patella tendon in his right knee. He admitted after the game that the injury might have ended his career.
Anthony Johnson added 21 for Atlanta, which shot 53 percent from the field and won for the sixth time in eight games.
Miami, which has lost eight of 11, was led by a season-best 36 from Dwayne Wade.
The Heat took a 111-108 lead in overtime on a three-point play by Wade with 1:46 to play. Atlanta then scored the game's final nine points.
The final points of regulation came on a jumper by Johnson with 57 seconds remaining.