James also had eight assists and seven rebounds while Chris Bosh finished with 14 points and six rebounds for the Heat, as the short-handed Bulls - again without Luol Deng and Kirk Hinrich - set a new franchise low for points in a play-off game.
"Chris is giving us just what we need," Miami coach Erik Spoelstra said on Bosh.
"He is giving us great presence at the rim with his rebounding and contesting shots."
Monday night's other game four encounter was a much tighter affair, but resulted in the Memphis Grizzlies also taking a 3-1 Western Conference semi-final series lead - thanks to a 103-97 overtime success against the Oklahoma City Thunder.
Mike Conley poured in a team-high 24 points while Zach Randolph and Marc Gasol each contributed 23 at FedExForum to push the defending Western Conference champions to the brink of elimination.
"We're not done yet," Randolph, said. "We're not done yet."
The Grizzlies can close this series out in Game 5 on Wednesday night back at Oklahoma City.