Hanging close until they finally caught New York midway into the final quarter, Celtics coach Doc Rivers kept telling his team that it would be defense that would make the difference.
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"I just said, `Guys, our defense is bailing us out. This is going to be a defensive win,"' Rivers said. "You rarely say you `steal a game' at home, but that's how it felt."
Kevin Garnett finished with 15 points and eight boards for the Celtics, who won for the seventh time in eight games.
Anthony scored 26, Tyson Chandler had 20 with 11 rebounds and Stoudemire had 16 with 11 rebounds for the Knicks. New York lost for the 11th time in 13 games.
"They were doubling and doing a good job. That's why other guys had to step up and make shots." New York coach Mike D'Antoni said about his team's final two shots.
Boston got the win despite shooting just 38.9 percent in the second quarter and 31.8 in third.
"It's good when you find way to win," Pierce said. "Things really weren't going our way."
Garnett grabbed his 10,000th career defensive rebound early in the second quarter, becoming the third player in NBA history to reach that mark. He's behind former Celtic Robert Parish (10,117) and Karl Malone (11,406).
Boston point guard Rajon Rondo returned after missing the previous eight games with a right wrist injury, but was ineffective, scoring just seven points and getting seven assists.
After Iman Shumpert's jumper from the right corner closed the score to 85-83, Allen nailed a 3 from the right wing. Following a putback by Chandler, Allen caught the ball in the right corner, drove the baseline and hit a left-hander that rolled in, giving the Celtics a 90-85 lead with just under 2 minutes left.
But the Knicks battled back, closing the gap to one after an alley-oop layup by Chandler and a steal and breakaway layup by Landry Field with 1:26 left.
Following a miss by Pierce, Anthony missed a drive, but the ball went out of bounds off Brandon Bass' hands, giving New York another chance.
But the Knicks turned it over. Pierce had what appeared to be an off-balance 3-pointer with 14.4 seconds left as the shot clock expired. But the officials overruled it following a reply review.
Fields missed a 3 from the left corner with 6 seconds left and Pierce grabbed the rebound and was fouled. He hit the first, but missed the second.
"It's right there. It's just the moment you get over that hump." Fields said. "Just got to get over it. Nothing much you can really say about it."
Steve Novak airballed a desperation 3 and Garnett batted the ball down the floor as time expired.
On Thursday, Stoudemire missed a shot from beyond his normal range -- a 3 with 11.9 seconds left that would have tied the score in a 105-102 loss to Chicago.
"It's definitely not a great feeling right now," he said. "Winning is always what we play the game for. It brings joy when you win. Right now we're not winning, so it's a little bit difficult to deal with."
Boston, which trailed since late in the opening quarter, tied it at 77 on Chris Wilcox's two free throws with 7:13 to play. The teams traded baskets and remained tied until Allen nailed a 3 from the right side with 4:24 to play. It was his first basket of the second half.
New York had a six-point halftime lead and increased it to 67-55 on Anthony's off-balance jumper midway into the third quarter. Both teams then played sloppily, turning the ball over numerous times and missing jumpers as the Knicks maintained at least a nine-point edge until late in the quarter.
Boston scored the final seven points of the third, cutting it to 72-69 after three when Wilcox had a putback of Pierce's miss at the buzzer.
With the crowd a little extra excited with the Patriots playing in the Super Bowl on Sunday, it appeared to help get the teams energized early, with both teams appearing to play tough defense from the start.
- Stoudemire had a season-high 34 points in a loss at home against Chicago on Thursday.
- Rondo was hit in the face with an elbow early in the game and had a welt under his right eye.
- With his team struggling to get wins, D'Antoni wasn't worried before the game about minutes with his team playing the second of three in three nights. "We'll see how everybody responds, but we need to win this game," he said. The Knicks host New Jersey on Saturday.
- Boston reserve G/F Marquis Daniels missed the game with a foot injury.
- Rivers joked about the Boston-New York rivalry. "A lot of love," he said, smiling, before talking about the Super Bowl matchup between the Patriots and Giants. "These two cities have a pretty good game coming up on Sunday, too."
- Rivers was given a technical in the second quarter and Stoudemire got one midway into the third after being called for an offensive foul.