Anthony, who was ejected during Friday's loss to the Chicago Bulls, finished with 33 points, scoring 19 in the fourth quarter, as the Knicks came from behind to secure the home win.
New York trailed for virtually the entire game before Anthony went on an 8-0 run in the final two minutes to put the Knicks up by four.
J.R. Smith scored 19 off the bench for New York (20-7) while Tyson Chandler had 16 and nine rebounds as the Knicks maintained their 5 1/2 game lead in the Atlantic Division.
Nikola Pekovic recorded 21 points and 17 rebounds to lead the Timberwolves (13-12), who were missing All Star Kevin Love due to an eye ailment. (Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)