Stoudemire went 10-of-15 from the field and grabbed six rebounds while Jason Kidd drained a pair of late 3-pointers en route to 12 points and eight rebounds as the Knicks came back from a 22-point deficit.
J.R. Smith provided 18 points, seven boards and seven assists and Steve Novak connected on four treys on his way to 15 points as New York won for the fourth time in five games.
Anthony -- tied for the NBA lead in scoring at 28.6 points per game -- hurt his knee when he tripped over his own feet in the second quarter and fell to the ground.
The extent of the injury was not immediately known.
The Cavaliers lost despite 23 points from Marreese Speights and 22 from Kyrie Irving, who returned from a three-game injury absence.