Miami has dropped back-to-back games for just the second time this season, having lost its previous encounter with Detroit on Tuesday. This was the opener of a four-game road trip and the Heat struggled without the services of Dwyane Wade.
Chicago has won only two of its 10 games on the road this year, but the victory over Miami gives the Bulls a 7-1 home record.
The consecutive losses for Miami follow a 10-game winning streak.
James scored 21 points and Michael Beasley had 15. Wade missed the game with flu-like symptoms.