Anthony drained 18-of-26 shots from the field, including seven 3-pointers, as the surging Knicks dealt Miami a rare home defeat and reeled off a ninth consecutive win.
Mario Chalmers also sat out the contest.
J.R. Smith (14 points) and Raymond Felton (10 points, nine assists) each reached double figures for New York, which tied Indiana for the No. 2 seed in the Eastern Conference with nine games to play.
Chris Bosh netted 23 points and Mike Millers supplied 18 with eight rebounds for Miami.