The Knicks opened the season by taking a 25-point lead at halftime and then survived a near collapse over the final two quarters.
It was a tie game with 2:30 to play when Tyson Chandler put New York in front for good at 82-81 by hitting a free throw.
A tip-in and layup on back-to-back possessions by Anthony gave the Knicks an 86-81 lead with 1:18 remaining.
Anthony scored 19 points and hauled in 10 rebounds while Raymond Felton added 18 points for the Knicks. After scoring 32 points in the second period to take their big lead, the Knicks produced just 34 over the final 24 minutes.