Mario Chalmers had 22 of his 29 points after the third quarter, including five in the third overtime.
Wade missed his second consecutive game after sitting out Wednesday night’s 118-83 win over Indiana. He hurt his foot at Charlotte on Dec. 28.
James was held out after he turned his left ankle late in the third quarter Wednesday night. He appeared to step on the foot of Indiana’s Paul George while attempting a fast-break layup. He still finished with 33 points and 13 assists.
Neither star was in uniform Thursday night.
Bosh, a former Georgia Tech star, hit a last-second, tying 3-pointer at the end of regulation to force the first overtime.
Joe Johnson had 20 points for the Hawks, who did not score in the third extra period.
Before the game, Heat coach Erik Spoelstra said Wade, who has a sore left foot, was “a little bit more unlikely” than James to play.
“We’re weighing everything: the schedule ahead, rest, how much treatment we can do,” Spoelstra said.
“Thankfully, these aren’t debilitating injuries.”
James Jones, who started in Wade’s place against Indiana, and Shane Battier started against the Hawks. Battier scored nine points and Jones had five.
Hawks coach Larry Drew said before the game that guard Tracy McGrady’s status was uncertain because of a bruised knee. McGrady did play and scored 14 points.
The Hawks had defeated the Heat 100-92 on Monday night in Miami, handing the Heat their only loss of the season.