MIAMI (AP) - On a night when the Miami Heat allowed more than 11 points over their season average, and against a team that has made scoring look amazingly easy over the last couple weeks, three plays in the final minute made all the difference.

And all were on the defensive end.

Mario Chalmers and Udonis Haslem each took a charge in the final 46 seconds, Dwyane Wade blocked a 3-point try by James Harden to essentially seal the outcome, and the Heat held off the Houston Rockets 114-108 on Wednesday night.

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``We held them to 108,' Heat coach Erik Spoelstra said. ``That team can score.'

The Rockets, who scored 140 points and tied an NBA record with 23 makes from 3-point range on Tuesday night against Golden State, have averaged 118.5 points in their last six games. Harden, who led all scorers with 36 points, scored 16 in the fourth quarter alone for the Rockets, who rallied from what was a 17-point deficit in the second half to make it a one-possession game.

But they never got closer.

Chalmers stepped in front of Harden to draw an offensive foul with 46 seconds left, and Haslem took one against James Anderson with 18 ticks remaining and the Heat hanging onto a three-point lead. Wade blocked Harden's shot with about 11 seconds left, and the Heat escaped with their 20th home win in 23 tries this season.

``We had a tough run scoring the basketball,' said Harden, who added 12 rebounds and seven assists. ``We even got stops, but the big plays where we needed to make a play, they got stops - so that was the difference in the ballgame.'

The Heat offense played a role as well, naturally.

LeBron James scored 32 points on 11 for 18 shooting, and Wade added 31 points and eight assists. Shane Battier scored 12, Norris Cole added 10 and Haslem - starting for Chris Bosh, who missed the game with the flu - grabbed 13 rebounds for Miami.

Houston got a 15-point, 14-rebound night from Omer Asik and 15 more points from Patrick Patterson. Jeremy Lin and Chandler Parsons each scored 13 for the Rockets, who were 9 for 25 from beyond the arc, one night after their record-tying show against the Warriors.

``They have no quit in them and it starts with their head coach,' James said of the Rockets. ``They've been through a lot and first of all, my condolences still to Kevin McHale and his family with what they've been through this year. It's very sad, but this team never gives up. They had 140 points last night and tied the NBA record in 3s, so we knew we had to defend the 3, but we made enough plays down the stretch and got enough stops.'

McHale was away from the Rockets for nearly a month earlier this season after his 23-year-old daughter died of complications from Lupus.

Wednesday's game had a distinct trend: Miami would try to take control, Houston would claw back.

And it held true all the way to the end.

Even with Miami up 12 with 6 minutes left, the Rockets had enough left for one more rally. Harden was fouled shooting a 3-pointer with 2:29 left, made all three shots, and the Rockets were within 104-101. Battier answered with a 3-pointer to restore Miami's six-point edge, and a 3 from Harden got the Rockets within 109-106.

That's when the Heat took charge - well, charges. And they were huge.

``You have to have great timing, great courage to put your body in there. But those were big,' Spoelstra said.

Wade and James both reached double digits in scoring by the end of the first quarter, with Miami ending the period up 32-30 after the teams shot a combined 63 percent. Houston, which was down by 10 in the first, used a 30-15 run to build a seven-point lead around the midpoint the second quarter, before the Heat closed the half on a 20-6 run to bring a seven-point lead into the locker room.

The third quarter was more of the same, with the Heat going on a big run, and Houston answering.

James, whose 13-for-14 effort from the field on Monday night came with him never venturing far from the rim to shoot - his average make that night being just over 3 feet in length - connected on three 3-pointers in the third. Two of them were in a 25-second span as the Heat opened on a 14-4 run that gave the reigning NBA champions a 77-60 lead.

And back came Houston.

The Rockets went on a 21-8 run to get within 87-83, and 3-pointer by Patterson opened the fourth-quarter scoring and cut Miami's lead to three. Miami answered with an 11-2 run, but predictably, that wasn't enough to put things away.

The Rockets had enough for one more run, and the Heat had enough to hang on one more time.

``They're one of the toughest teams to guard,' Wade said. ``To win this game, we had to get stops - key stops. And I thought we were able to do that.'

NOTES: James made his first three shots on Wednesday, meaning he made 17 of 18 shots from the field in a span that started with his last attempt at Toronto on Sunday. ... All five Rockets starters scored in double figures, the third time in the last four games that's happened. ... James scored his 5,000th point in a Heat uniform, the ninth player to do so. He did it in 187 games, 31 fewer than Wade needed to score 5,000 for the franchise. ... Nick Aquilino, the son of Heat neuromuscular therapist Vinny Aquilino, performed the national anthem.