New York hit 57 percent of its shots from the field, including 16-of-27 from 3-point range, and broke the game open by outscoring the Nets in the third period 34-16.
Brooklyn lost for the ninth time in 11 games in a matchup of the two worst teams in the Atlantic Division, where the five clubs have a combined record of 30-62.
Even though New York has won only four times all year, the Knicks trail division-leading Boston by only 2 1/2 games.
Anthony made 8-of-12 from the field and scored 19 points. Iman Shumpert added 17 points, making five from beyond the arc, and Andrea Bargnani had 16.
Brook Lopez delivered 24 points to lead Brooklyn. It was the first of four meetings this year between the Knicks and Nets. They split their four contests last season.