New York's Anthony and Boston's Garnett had jawed at each other throughout a testy contest earlier this month, which continued after the game when Anthony tried to confront Garnett at the Boston team bus. Anthony received a one-game suspension for his role in the incident.
On Thursday, the pair exchanged a fist bump before the tip-off and were all about business.
Anthony led the way with a game-high 28 points while Amar'e Stoudemire, Jason Kidd and Iman Shumpert all reached double figures to help the Knicks (26-14) cement their place at the top of the Eastern Conference's Atlantic division.
Garnett was restricted to just eight points, but also contributed 12 rebounds for Boston.
Celtics point guard Rajon Rondo added 23 points, 10 rebounds and 11 assists while Paul Pierce weighed in with 22 points as the home team slipped to 20-22 for the season with their fifth straight defeat.
There were 17 lead changes but none in the final quarter as Anthony hit the 20-point mark for his 21st straight game.
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