James also dished off eight assists and grabbed seven rebounds for the Heat, who pushed Chicago to the brink of elimination in their best-of-seven Eastern Conference semifinal series.
Chris Bosh added 14 points and six boards for the Heat, who used a stifling defense to hold the Bulls to a playoff franchise low in points and field goal percentage (25.7 percent).
Miami yielded only nine points in the third quarter -- another all-time low for Chicago.
The Heat will seek to close out the series at home in Wednesday's Game 5.
Notable deaths of 2014 [PHOTOS]