Green made 6-of-7 from the field during the final 12 minutes, allowing the Hawks to hold on and snap a two-game skid.
It was only the second loss in 10 games for the Knicks since Mike Woodson took over as interim coach in place of Mike D'Antoni. New York's advantage over Milwaukee in the battle for the eighth and final playoff spot in the Eastern Conference was reduced to 1 1/2 games.
New York was led by Carmelo Anthony with 36 points and Iman Shumpert had 25. Point guard Jeremy Lin missed his third straight game with a sore knee.
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