After knocking the Celtics from the top of the Atlantic Division, the Knicks took the first step to knocking them out of the playoffs by holding Boston to three baskets and eight points in the final period.
Anthony, the NBA's scoring leader, shot only 13 for 29 from the field but scored eight points in the fourth quarter, including consecutive baskets late in the period that finally gave the Knicks breathing room in a tight game.
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.
Kevin Garnett had eight points and nine rebounds but shot only 4 of 12 from the field. Jason Terry, another veteran on a young Celtics team, missed all five shots off the bench.
CLIPPERS 112, GRIZZLIES 91
LOS ANGELES (AP) — Chris Paul led seven players in double figures with 23 points, Eric Bledsoe had 15 and the Clippers beat the Grizzlies while getting just one dunk in their playoff opener.
Chauncey Billups scored 14 points, and Caron Butler and Jamal Crawford had 13 apiece on a night when Blake Griffin was held to 10 points and five rebounds before fouling out with 3:32 left as Lob City was grounded.
Reserve Jerryd Bayless led the Grizzlies with 19 points, Marc Gasol had 16 and Zach Randolph had 13 points and four rebounds while playing with five fouls in the rematch of last year's first-round series, won by the Clippers in seven games. Bayless was one of four Grizzlies with four fouls.
Game 2 is Monday night at Staples Center.
Memphis closed within a point early in the fourth on a 3-pointer by former Clipper Keyon Dooling. Los Angeles answered with a 15-3 run to go up 92-79, equaling the 13-point lead it had in the first half. Eric Bledsoe, who had seven points, opened and closed the spurt with layups as the reserves played an important role in the key stretch.
NUGGETS 97, WARRIORS 95
DENVER (AP) — Andre Miller scored a playoff career-high 28 points and sank a nifty layup with 1.3 seconds left that lifted the Nuggets to the win in Game 1 against the Warriors.
Miller drove left past rookie Draymond Green, did an up-and-under between two defenders under the basket and banked the ball off the glass with his right hand.
Golden State inbounded the ball and Stephen Curry's desperation 3-pointer wasn't anywhere close as the horn sounded and Denver celebrated its 24th straight win at the Pepsi Center.
Miller scored 18 in the frenetic fourth quarter.
Game 2 is Tuesday night at the Pepsi Center, where the Nuggets posted an NBA-best 38-3 home record during the season.
NETS 106, BULLS 89
Deron Williams, Brook Lopez and the Nets turned the Brooklyn blackout into a blowout.
Williams scored 22 points, Lopez had 21 and the Nets ripped apart the Bulls' vaunted defence with a spectacular second quarter, when they made 16 of 20 shots.
Joe Johnson finished with 16 for the Nets, who made their successful first season in Brooklyn even better with a victory in their first playoff appearance since 2007. They will host Game 2 on Monday night.
The Nets wore their road black uniforms and fans were encouraged to wear black as well to make it a "blackout" for the first major post-season game in Brooklyn since Oct. 10, 1956, when the Yankees beat the Dodgers in Game 7 of the World Series at Ebbets Field.
Carlos Boozer had 25 points and eight rebounds for the Bulls, who had Joakim Noah in the starting lineup despite foot pain. But he was clearly limited, and there was no reason to play him more than the 14 minutes he got with the game never in doubt after halftime.