Bam Adebayo had 20 points and 10 assists for the Heat, and Jimmy Butler added 20 points.
Miami trailed but saw what was a 24-point lead cut to two in the final moments. Coby White scored 31 points for Chicago, and Nikola Vucevic had 26 points and 14.
The Bulls outscored the Heat 60-45 in the second half, but wound up losing for the seventh time in their last 10 games. The teams will meet in Miami again Monday.