The team announced before the game Stoudemire, a six-time all-star forward, would be out of the lineup indefinitely with a bulging disc.
New York was also without point guard Jeremy Lin, who is nursing a sore knee.
Anthony stepped up with a big game while Tyson Chandler and Baron Davis added 13 points apiece for the Knicks, who padded their lead to 2 1/2 games over the Bucks in the race for the final Eastern Conference playoff spot.
New York improved to 7-1 under interim head Coach Mike Woodson.
Mike Dunleavy scored 26 for Milwaukee, which fell for third time in four games.