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Celtics-Heat: 56k | 300k 
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Miami forward Brian Grant sat out for the first time in 124 games due to a left knee contusion, but Haslem and Odom picked up the slack, combining for 31 rebounds and helping the Heat to an overwhelming 52-34 edge on the glass.
But neither player grabbed the biggest rebound of the game with Miami clinging to an 85-84 lead in the final minute. Pierce missed a jumper from just inside the 3-point line and Blount, who had 16 points, outjumped Haslem and followed the shot to put Boston in front.
"I just happened to be in position to get the shot in," Blount said. "Just a matter of staying with the play."
"We were scrambled in transition," Miami coach Stan Van Gundy said. "(Blount) was in really deep, but somebody had to put a body on him. We should have blocked him out on that play."
Eddie Jones missed a 3-pointer for the Heat and Celtics guard Mike James made 1-of-2 free throws with eight seconds left. Miami's Rafer Alston attempted a 3-pointer that barely grazed the rim as time expired.
"We had the game won and we threw it away," Odom said. "We didn't get the loose balls and rebounds when we had to. This one hurt."
Pierce scored 10 of his 29 points in the fourth quarter and Walter McCarty added 14 for Boston, which snapped a four-game losing streak, avoiding their longest slide of the season.
"We knew this was a must-win for us and we just had that sense of urgency to get it done," Pierce said.
Haslem had 18 points and a career-high 17 rebounds and Odom collected 12, 14 and nine assists for the Heat, who lost for the sixth time in seven games.
"Udonis was fabulous tonight," Van Gundy said. "He was clearly our best player and gave us a lift. You can't do much better than his effort tonight."
"Personally, the loss takes away from everything," Haslem said. "I don't worry about my numbers, just the way I play and going out there and doing what it takes."
Miami had a 79-70 cushion with 5:38 remaining, but Boston scored 16 of the game's final 21 points. McCarty and James sparked the comeback with back-to-back 3-pointers before Pierce took over.
Pierce buried a jumper and split two free throws before making a spinning layup to bring the Celtics within 84-83 with 72 seconds left.
"We could have gotten discouraged when they went up by eight or nine with five minutes left," Pierce said. "But we kept our composure and kept up our defense."
Odom, who made just 4-of-17 shots, missed a short jumper at the other end, setting up Boston for the decisive basket.