With star Derrick Rose suffering from a sprained ankle and out of action for the 15th time in 18 games, the Bulls saw their lead over the Heat dwindle to 1 1/2 games in the fight for the best record in the Eastern Conference.
Miami had only a two-point lead with 9 minutes to play but closed the game on a 15-6 run and limited the Bulls to 11 points in the fourth period.
James had 11 rebounds and six assists while Dwyane Wade added 18 points and Mario Chalmers contributed 16.
The Heat's Chris Bosh missed his second straight game. The team has not specified an injury for Bosh, saying he is being rested for the playoffs.