NEW YORK -- Carmelo Anthony started fast, struggled through the middle and finished with a flurry.
Anthony scored 36 points, leading the Knicks to an 85-78 victory on Saturday in their playoff opener.
"It's a wonderful feeling to know that we got our first win of the series here on our home court, took care of that business," Anthony said. "It was real important for us to come out and get this first win."
The NBA's scoring leader had 10 quick points and endured a tough shooting night from there before scoring eight points in the fourth quarter, helping New York take a 1-0 lead in a series for the first time since the 2001 first round against Toronto.
"Boston knows Melo and they know he's not going anywhere, but they're going to make it as tough as possible for him to score the ball," Knicks coach Mike Woodson said. "And he got off to a good start and then he had that slow middle, and then when he had to pick it up down the stretch, he made the plays that we needed him to make. And I mean that's what the great ones do. They figure it out and Melo's done that all season for our ballclub."
Anthony shot only 13 of 29 from the field but made consecutive baskets late in the final period, when the Knicks held Boston to three baskets and eight points.
Game 2 is Tuesday night before the Celtics host Game 3 on Friday in what will be their first home game since the Boston Marathon bombings.
Jeff Green scored 26 points and Paul Pierce added 21 for the Celtics, who badly missed injured point guard Rajon Rondo, committing 21 turnovers that led to 20 points. The Knicks got their hands on the ball at will in the fourth quarter, when Boston shot 3 of 11.
"We had some just bad turnovers tonight," Celtics coach Doc Rivers said. "If we had those turnovers in any game, we probably should lose the game and we did. We were making post passes from the other side of the floor. I mean, those are just not good passes."
The Celtics led after three quarters and tied the game for the final time at 72 on Garnett's basket with 8:13 remaining. Anthony then made consecutive jumpers, and after the Celtics got back within three later in the period, he made a layup and a long jumper that gave New York an 83-76 advantage with 1:21 left.
Green made two free throws and the Celtics double-teamed Anthony, but he fired a pass to a wide-open Kenyon Martin under the basket to put it away with 40 seconds left.
"We just panicked a little bit. We don't have to do that," Celtics guard Avery Bradley said. "We have to keep our composure and play the right way. We didn't."
J.R. Smith scored 15 points and Raymond Felton had 13 for the Knicks, while Martin finished with 10 points and nine rebounds in huge minutes for New York with Tyson Chandler struggling through a scoreless 20 minutes after barely playing late in the season because of a bulging disk.
The Knicks ended the Celtics' five-year reign as Atlantic Division champions by going 54-28, winning their first division title since 1994 with their most victories since going 57-25 in 1996-97. The next step would be playoff success for New York, which hasn't won a postseason series since 2000 and couldn't even get a game against the Celtics two years ago.
The Celtics wore a special patch recognizing the difficult week in Boston following the bombings that killed three people at the Boston Marathon on Monday. Rivers said many players were calling home to check on their families Friday, when the Boston area was in lockdown while authorities searched for the suspect. That even affected the Celtics, as Rondo, out for the season with a knee injury, was unable to join the team Friday in New York because he couldn't get out.
The Boston Fire Dept. Color Guard and FDNY color guard carried the flags onto the court before the national anthem, and Anthony and Pierce addressed the crowd before the game, with a few fans booing Pierce before many others yelled "Shhh!" so he could speak.
"Boston will rise and run again," Pierce said.
Fans were supportive of Boston but not the Celtics, as Rivers expected. Garnett, whose clash with Anthony in a regular-season meeting resulted in a one-game suspension for Anthony after he attempted to confront Garnett outside the Celtics' team bus, was loudly booed.
The Knicks threw up airballs on their first two attempts -- Chris Copeland was woefully short on their first shot. But Anthony quickly got them untracked, hitting a pair of jumpers and then consecutive 3-pointers in a 12-2 spurt for a 12-6 lead. But Boston regrouped and rallied to take a 29-26 lead on Green's 3-pointer as the first quarter ended.
It was close throughout the second, but the Knicks' offense stalled late in the period, with too little ball movement and too much of Anthony holding the ball. Green scored 12 in the period and Boston led 53-49 at the break.
The Celtics opened a 70-63 lead late in the third, but New York got the final four points of the period, then opened the fourth with Felton's jumper and Martin's three-point play to go back ahead, 72-70.
The Knicks were without starting guard Pablo Prigioni because of a sprained ankle, and rookie Copeland was scoreless in his place. The Knicks were 16-2 with Prigioni in the starting lineup during the season.
The Knicks won three of four meetings in the regular season, winning the series for the first time since 2003-04. ... The Celtics announced multiple initiatives to support victims affected by the Boston Marathon tragedy. Their Shamrock Foundation has committed to raise $200,000 to support The One Fund Boston through a $100,000 pledge from the foundation and multiple team initiatives to raise an additional $100,000. ... Jets quarterback Mark Sanchez was at the game and loudly booed when shown on the overhead video screen. Even Sanchez appeared to laugh.