The Bulls did just fine on Thursday, although things got a little tight down the stretch.
Miami cut it to 93-81 on Norris Cole's runner with 5:38 remaining. But Gibson answered with a jumper and blocked a layup by Udonis Haslem.
Deng made a 3 with just under four minutes left to make it 98-81, and Chicago hung on from there.
Before that, the only tension came early in the third quarter when Hinrich took a shot to the neck from Cole away from the ball. The result was an angry exchange, a flagrant foul one for Cole and a technical for Hinrich.
The Bulls' guard hit both free throws after James missed a foul shot, making it 67-45.
Boozer led a scorching start by Chicago, scoring 19 points as the Bulls built a 58-44 halftime lead.
But in the end, it was the Bulls' rebounding and defense that had the Heat shaking their heads.
"We've never been a great rebounding team but we've been able to overcome that," James said. "Teams have done a much better job of rebounding against us. It could be an effort thing, it could be a lot of things but we just got to go out and just go get them.
"I'm going to do a better job of that, get more rebounds. But it's a group thing for a team. We don't have a Kevin Love or Joakim Noah or Dwight Howard, those types of guys who can get you 15-plus, we have to do it as a collective group."
NOTES: There was a moment of silence before the game to honor Nelson Mandela, who died Thursday at the age of 95. ... This was the Bulls' most lopsided win over the Heat since a 126-96 blowout at Miami on Jan. 16, 2008. ... Andersen expected to rejoin Miami on Friday in Minnesota. The Heat play the Timberwolves on Saturday.