James, who left Quicken Loans Arena in disgust following an embarrassing loss to Golden State on Sunday, added 12 assists and outshined fellow superstar and good friend, Dwyane Wade, who scored 22 points but didn't make his first field goal of the second half until there was only 4:01 remaining.
By then, the Cavs were already by 12 points and they went on to win for just the fourth time in their last 14 games. Anderson Varejao scored 15 points and Zydrunas Ilgauskas 13 for Cleveland, which had one of its most balanced games this season.
Wade finished just 7-of-18 from the floor and 8-of-16 from the free-throw line for Miami, which began the season as one of the Eastern Conference's favorites but is headed in the wrong direction.
About the only positive for the Heat was that Shaquille O'Neal didn't foul out. The Heat's big man had been disqualified from his previous five games, coming within one of matching the NBA record set by Milwaukee's Don Boven in 1952.
O'Neal picked up his fifth foul with 6:55 left and was immediately pulled by coach Pat Riley. Ricky Davis had 15 points and O'Neal 13.
Looking for a quick fix, Cavs coach Mike Brown resorted to a starting lineup that helped Cleveland to its first conference title last season. He replaced Gibson with Hughes, who had been coming off the bench, at point guard alongside Sasha Pavlovic.
Hughes had only four points but he played excellent defense and contained Wade, who never got a chance to go off.
But the biggest change for Cleveland was a defensive intensity that has been missing most games this season.
Trailing 59-52 midway through the third, the Cavaliers upped their defensive pressure and it paid off as the Heat began turning the ball over with sloppy passes, charges and assorted violations.
Cleveland bolted to a 15-0 lead, capped by a steal and thunderous breakaway dunk by James to take a 67-59 lead with 1:50 left in the third. The spurt woke up a slumbering crowd and it allowed the Cavs to take a lead into the fourth quarter for just the seventh time in 29 games.
Gibson then opened the fourth with a pair of 3-pointers and with the Heat misfiring, the Cavaliers pushed their lead to 88-72 on Varejao's layup with 4:19 left.