Anthony finished with 30 points, but left the game in the third quarter with a sprained left ankle. It was his third consecutive 30-point performance.
The Knicks owned a 41-27 lead after the opening period and held on from there to win their third in a row. It was New York's 17th victory of the season, three more than any other team in the Eastern Conference.
Los Angeles, meanwhile, lost its fourth straight and fell to 2-8 on the road.
Anthony had three 3-pointers in the first period and wound up 10-of-15 from the field. Robert Felton added 19 points while both Tyson Chandler and J.R. Smith had 18 for the Knicks.
New York remained unbeaten in nine home games and is the only NBA team without a home loss this year.
Kobe Bryant led the Lakers with 31 points and 10 rebounds, but he was only 10-of-24 from the field.
New York shot 53 percent to 41 percent for the Lakers. New York turned the ball over just six times.