James grabbed seven rebounds and handed out six assists while Chris Andersen contributed 15 points off the bench for the Heat, who got revenge on Chicago after the Bulls ended their 27-game winning streak last month.
Mario Chalmers scored 15 points for Miami, which shot 51.4 percent from the field en route to a sixth consecutive victory and a club record-breaking 36th straight at home.
Luol Deng scored 19 points for Chicago, which fell one game behind Atlanta for the No. 5 seed in the Eastern Conference with two games left to play.
Carlos Boozer had 16 points and 20 rebounds for the Bulls.