Anthony landed 23 of 35 field goals with six three pointers and was 10 from 10 from the free throw line to post the highest single player tally since Kobe Bryant notched 65 points in 2007.
He topped Bryant's Madison Square Garden record of 61 points set five years ago and beat Bernard King's Knicks' record of 60 points.
"I was just taking it one possession at a time," Anthony said. "I came into the game locked in. I didn't know I was going to have this type of performance. It's an unbelievable feeling.
"It's just a zone you get into sometimes. Only a certain group of people know what that zone feels like. Tonight was one of those zones. My team mates saw that.
"It didn't really sink in exactly what I did tonight. I know Bernard King is somewhere smiling at me right now."
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Thunder 101, Celtics 83
No Kevin Durant or Russell Westbrook? No problem for the Oklahoma City Thunder.
With Durant, who is leading the NBA in scoring at 31 points per game, nursing a bruised right shoulder and Westbrook out after knee surgery, the Thunder flashed the rest of their weapons and cruised to a 101-83 victory over the Boston Celtics.
The win was the sixth straight and seventh in the last eight games for the Thunder (34-10).
Forward Serge Ibaka had 21 points and seven rebounds and swingman Jeremy Lamb came off the bench with 19 points, six rebounds and three assists to lead the Thunder.
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Clippers 112, Bulls 95
Forward Blake Griffin tallied 26 points and 13 rebounds as the hot-shooting Los Angeles Clippers beat the Chicago Bulls 112-95.
The Clippers (30-15) knocked down 10 of their first 11 attempts from three-point range and the Bulls never got closer than eight points after falling behind 41-26 in the first quarter.
Guard Jamal Crawford added 19 points, guard J.J. Redick scored 18 and guard Darren Collison finished with 17.
Forward Carlos Boozer led the Bulls (21-21) with 22 points.
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Spurs 105, Hawks 79
San Antonio used the inside-out punch of center Tim Duncan and guard Patty Mills to prey on the injury-depleted Atlanta Hawks and take a 105-79 win.
The 6-foot-11 Duncan scored 17 points and had 16 rebounds for his 17th double-double and Australian Mills scored 18 points, including a career-best six three-pointers, as the Spurs swept the season series against Atlanta.
Atlanta (22-20) was led by forward Paul Millsap with 15 points and eight rebounds.
San Antonio (33-10) also got 18 points from forward Boris Diaw and 11 points and seven assists from guard Tony Parker.
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Grizzlies 88, Rockets 87
Houston Rockets forward Chandler Parsons set an NBA record for three-pointers in one half but the Memphis Grizzlies relied on their defense late and held on for an 88-87 victory.
Grizzlies forward James Johnson converted a reverse layup with 1:58 remaining to give Memphis (21-20) an 88-84 lead.
Parsons followed with his 10th trey, setting the franchise record and capping his career-best 34-point night to close the deficit to one point.
But Parsons missed a three with 1:13 remaining as Houston mishandled several scoring opportunities, including a desperation Patrick Beverley trey at the buzzer.
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Magic 114, Lakers 105
Forward Tobias Harris had 28 points and 20 rebounds, both season highs, to lead the Orlando Magic to a 114-105 victory over the struggling Los Angeles Lakers.
It was the 11th consecutive game the once-proud Lakers (16-28) have allowed at least 100 points.
They have lost nine of their last 11 games and it was just the second time this season the Magic (12-32) won when an opponent scored 100 or more.
Magic guard Arron Afflalo had 23 points while the Lakers were led by center Pau Gasol, who had 21 points and 11 rebounds.
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Raptors 104, 76ers 95
DeMar DeRozan scored 34 points and Kyle Lowry had a triple-double as the Toronto Raptors defeated the Philadelphia 76ers 104-95.
Lowry, a Philadelphia native and Villanova University graduate, finished with 18 points, 13 assists and 10 rebounds for the Atlantic Division-leading Raptors (22-20), who won their second straight and ended a four-game road losing streak.
Point guard Michael Carter-Williams had 20 points to lead Philadelphia (14-29), which lost for the fourth time in five games.
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Pelicans 103, Pistons 101
Guard Eric Gordon's layup in the final second gave the New Orleans Pelicans a 103-101 win over the Detroit Pistons.
Guard Anthony Morrow scored 13 of his 21 points in the fourth quarter for the Pelicans (17-25), who trailed by 16 late in the third quarter.
Gordon and guard Austin Rivers added 15 points apiece and forward Anthony Davis chipped in 14.
Point guard Brandon Jennings scored 22 of his game-high 28 points during the second half to carry the Pistons (17-26), who have lost eight of their last nine home games.
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Nets 107, Mavericks 106
A career-high 34 points from forward Mirza Teletovic was just enough to ensure the Brooklyn Nets are still the hottest team in January.
A 107-106 win over the Dallas Mavericks helped improve the Nets to 9-1 in 10 games this month.
Teletovic single-handedly kicked a sluggish game into gear and gave his side its insurmountable lead with a big-time second quarter.
The Bosnian hit his first three, three-pointers, all in succession, as he posted 24 points in the frame, including a career-high 19 in his first six minutes.
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Cavaliers 93, Bucks 78
Center Anderson Varejao had a game-high 16 points in the Cleveland Cavaliers' 93-78 victory over the hapless Milwaukee Bucks.
Power forward Tristan Thompson recorded his 21st double-double of the season with 14 points and 10 rebounds for the Cavaliers (16-27).
Guard Kyrie Irving posted his fifth double-double with 10 points, 10 assists and three rebounds.
Swingman Khris Middleton had a team-high 13 points for the Bucks (8-34).
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