Miami, who dominated the Bulls 115-78 in Game 2, started with an 11-2 run in Monday's contest and never looked back.
"We just try to wear a team down throughout the series and get better each game," said James who was the leading vote getter in balloting for the NBA All Defensive Team on Monday. "We've done a great job of closing out quarters and going into the next quarter with momentum."
Chicago shot a dismal 25.7 percent from the field and also scored a postseason franchise low in points in front of a crowd of 21,990 at the United Center arena.
The Bulls scored just nine points in the third quarter, another franchise low.
Miami can now close out the best-of-seven series in game five Wednesday at home.
"We have to come out with the same intensity that we came out with tonight, both offensively and defensively," James said.
Chris Bosh also scored in double figures, finishing with 14 points and four blocks for the Heat who had 19 fastbreak points compared to just seven for the Bulls.
"We wanted to work as hard as we could on defence tonight," Bosh said. "We are looking forward to having a chance to close these guys out Wednesday."
Carlos Boozer had 14 points and 12 rebounds for the Bulls, whose previous play-off franchise low in points (69) came against the Detroit Pistons in game one of a 2007 NBA quarter-finals.
Their previous low in field-goal percentage (31.1 per cent) also came against the Pistons in Game 7 of the 1990 NBA semi-finals.
Boozer shot just three-of-14 and Nate Robinson was zero-for-12 and did not score.
"We are disappointed with the way we played," said Joakim Noah. "But there is still basketball left and we are not giving up."
Once again, the Bulls had to play without injured star Derrick Rose, Luol Deng and Kirk Hinrich.
Rose has not played all season and Deng underwent a spinal tap two weeks ago to rule out meningitis and has been slow to recover.
With all of the injuries and the heavy minutes, Chicago appears to be losing steam.
"We have to bounce back," said Bulls' coach Tom Thibodeau.
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