Playing without defending league MVP Derrick Rose, the Bulls defeated the Heat for the first time in six tries in a meeting of the top two teams in the Eastern Conference.
Rose missed the game with a groin strain, but Lucas scored 24 points off the bench while making 9-of-12 shots from the field. He scored 11 points in the fourth quarter.
Miami has lost back-to-back games and has dropped four in a row on the road.
Dwyane Wade had 36 points for Miami and LeBron James scored 35.