Chris Bosh scored 24 points and added 12 rebounds for the Heat, who never trailed — but this win in a rematch of last season's Eastern Conference finals was not easy. Dwyane Wade added 15 points for Miami.
Rose scored 34 points for Chicago, but missed a pair of foul shots that would have given Chicago the lead with 22.7 seconds left. He had made all 29 of his free throws in the fourth quarter this season.
And Rose had a shot to tie in the final seconds, but his short jumper bounced off the rim.
Bosh sealed it with two free throws with 0.1 seconds left for Miami, which has now won five straight over the Bulls — counting the last four games of last season's East title series.
Both sides said this game was supposed to be just another regular-season matchup, one without extra meaning.
So not true.
The Bulls erased what was a 12-point deficit and tied the game at 84 on a brilliant layup by Rose with 6:55 left. The Heat answered with a 10-2 run, before Rose's three-point play with 49.1 seconds left cut the lead to 94-93.
Rose then lost the ball on a drive, but drew contact from Miami's Udonis Haslem and went to the line with Chicago down one with 22.7 seconds left. Rose's first hit the front of the rim and bounced away, and his second rimmed out. James grabbed the rebound and was fouled by Joakim Noah — only to miss both free throws himself.
After the second miss, Bosh appeared to emerge with the rebound, but an inadvertent whistle led to a jump ball. James outleaped Taj Gibson, getting the ball to Mario Chalmers, who made one free throw for a two-point lead.
Chicago wound up getting one last chance with 9.9 seconds left, calling time-out. Naturally, it went to Rose, who weaved his way into the lane — but came up short. Bosh got the rebound, and Miami began celebrating.
Rip Hamilton and Noah each scored 11 for Chicago, which got 10 apiece from Ronnie Brewer and Carlos Boozer.
The Bulls played without forward Luol Deng and guard C.J. Watson, both sidelined with wrist injuries. Watson may be back in Chicago's lineup as early as Monday, and Deng — who has a torn ligament in his left, non-shooting, wrist — is "very close" to a return, Bulls coach Tom Thibodeau said.
Miami took an 11-point lead early in the fourth on back-to-back 3-pointers from Shane Battier and James. The Bulls roared back, as they did for most of the day whenever the Heat seemed on the cusp of taking control.
They just never got the lead, despite Rose's best efforts.
"Two sick moves by D-Rose," Oklahoma City's Kevin Durant tweeted as he watched the game, marveling at two layups by Rose that knotted the game at 84.
Insistence that this was "just another game" notwithstanding, Miami started quickly. Wade appeared a bit more emotionally charged than usual after joining his teammates in the pregame huddle, and the Heat ran out to a fast early edge.
Maybe it would be more accurate to say they "jumped" out to that lead.
Wade set James up for three dunks in the first 7 minutes, the last of which is probably going to be replayed for quite a while. James appeared to be forgotten as he hovered on the weak side of the floor, so he darted toward the basket. Wade tossed a lob his way — and the two-time MVP leapfrogged the 5-foot-11 John Lucas for a dunk that put Miami up 16-7.
Even the NBA took notice of that one: Within minutes, replays of the James dunk were sent out on the league's Twitter feed.
Chicago quickly settled down, getting within 24-22 at the end of the first quarter. But Miami scored 11 straight early in the second, the last seven of those coming with Wade and James both on the bench, to open a 35-24 edge. Wade's first points came with 6:14 left in the half, two free throws that gave Miami what was its biggest lead at 42-30.
The Bulls chipped away again, and by halftime Miami's edge was only 56-51.
Wade missed eight of nine shots in the first half and an airball dropped him to 1 for 10 early in the third quarter.
Chicago had a chance for its first lead when Rose attacked the rim moments later. But his layup was blocked by Joel Anthony, and James threw about a 65-foot pass to Wade for a dunk. James found Wade again for another transition slam less than a minute later for a 63-58 advantage.
The lead was still five entering the fourth. James made a 20-footer over Brewer with 0.2 left in the third to push Miami's edge to 76-71.
Notes: James had a large icepack strapped to his right shoulder during a first-half stint of rest. He was grabbing at the shoulder in pain early in the first quarter after a collision, but did not appear to have a serious issue. ... Boozer said he needed more than 20 tickets for the game. He's been spending part of his offseasons in Miami for several years.