HOUSTON (AP) -- LeBron James was wiped out - and it showed.
James had a chance to tie the game with a desperation 3-pointer at the buzzer, but it was off - just like most of his second-half shots.
The four-time MVP finished with 22 points, one night after setting a club record with a career-high 61 against Charlotte. He acknowledged before Tuesday's game that he was ''extremely tired'' and that he spent most of the day sleeping.
James had 19 points by halftime, but appeared to drag at times in the second half and spent the first half of the fourth quarter on the bench. He was 1 for 7 after the break.
''I fought through it in the first half. Second half it just wasn't there for me,'' James said. ''Got out of rhythm.''
Still, the Heat cut their deficit to three when Michael Beasley hit a 3-pointer with 21.2 seconds left. Harden threw the ball away after that, and Howard accidentally hit James in the face when they both went up to try to grab a long pass.
James lay on the court holding his broken nose for a few seconds before getting up and slowly walking to the bench. He has been wearing a protective mask to protect his nose.
James remained in the game after a timeout, then missed the desperation 3 with Howard in his face.
''I knew I had to put up a heave over top of him,'' James said. ''I felt like I got a good look - just a little long.''
The Rockets used the word composed repeatedly after the game to describe their play.
''There's no need for us to get worried,'' Howard said of the team's mindset after Beasley's 3. ''Situations like that, the best thing we can do is stay composed. If we point our finger or put our heads down, it gives the other team confidence. That's something we've been trying to work on all year.''
Dwyane Wade had 24 points for the Heat after sitting out Monday night. Beasley also scored 24, a season high.
Miami never led, but tied it twice in the fourth quarter. Houston used an 11-2 spurt to take a 104-95 lead with less than 3 minutes remaining.
''We were able to push back in the fourth quarter and tie the game up,'' Wade said. ''But we had to exhaust so much energy trying to come back.''
Houston led by 13 early in the fourth before two separate runs by the Heat tied it at 91 with 7 minutes remaining. The also tied it at 93 before Houston used its late run to close it out.
''We did some good stuff,'' Rockets coach Kevin McHale said. ''We made some plays. ... I thought during stretches in this game we played really well.''
The Heat had made consecutive 3-pointers to cut the lead to seven early in the fourth quarter when Chris Andersen blocked a shot by Donatas Motiejunas. Andersen stood under the basket after the block and taunted Motiejunas, drawing a technical foul.
Miami then used an 8-0 run, which included a 3 by Beasley, to cut it to 88-87 with 8 1/2 minutes left.
Houston opened the second half with a 9-2 run capped by Chandler Parsons' dunk over James. Shane Battier had a basket for Miami after that, but Houston reeled off six straight points to extend the lead to 68-56.
An airball on a 3-point attempt by Wade was one of three missed shots by the Heat in that span.
The Rockets were up by nine soon after that when Harden launched a long alley-oop to Howard, who barely grabbed it in time to sail over Chris Bosh for the dunk.
Howard picked up a foul with about 5 minutes left in the first half when he ran into James as he was driving to the basket, causing him to lose control of the ball, which bounced off James' mask.
A reverse layup by James and a free throw by Wade in the last 20 seconds of the first half cut Houston's lead to 53-52 at halftime.
The Rockets jumped out to a 7-0 lead and were up 39-32 at the end of the first quarter.
NOTES: Hall of Fame center Hakeem Olajuwon, and Houston Texans stars Andre Johnson and Arian Foster attended the game, as did Minnesota Vikings running back Adrian Peterson and former Astros pitcher and seven-time Cy Young Award winner Roger Clemens. ... James said the best compliments he received following his big game against Charlotte came from the two most important women in his life. ''My mom and my wife saying how proud they were of me and that I never cease to amaze them,'' he said. ''So it's always great when your family gives you that type of gratitude and response.''