Green scored 15 of his 20 points in the final period, including a 3-pointer from the corner that stretched Atlanta’s lead to 94-84.
Woodson, who coached the Hawks from 2004-10, returned to Philips Arena for the first time as the Knicks interim coach. His team wasn’t at full strength, forced to go without injured starters Amare Stoudemire (back) and Jeremy Lin (left knee).
Carmelo Anthony led the Knicks with 36 points and rookie Iman Shumpert matched his career high with 25. Still, the Knicks lost for only the second loss in 10 games under Woodson.
The Hawks got much more of a team effort than the short-handed Knicks. Josh Smith added 23 points, Marvin Williams 13 and Jeff Teague 11 to go along with seven assists. Zaza Pachulia handled the dirty work, grabbing 12 rebounds to help the Hawks to a 40-33 edge on the boards.
Anthony and Shumpert were about it for the Knicks. No one else scored more than seven points, and New York struggled mightily at the foul line (22 of 33). The Hawks, by comparison, knocked down 22 of 26.
Both teams were sloppy with the ball, but Atlanta did a better job taking advantage of the turnovers with 27 points off New York’s 18 giveaways. The Hawks’ 17 turnovers led to 17 points for New York.
Atlanta built a 15-point lead in the first half and seemed on the verge of blowing it open again on a couple of acrobatic plays by Smith that fired up the crowd.
Green, averaging 7.0 points a game off the bench for Atlanta, made all but one of his seven shots, including the huge trey with 3½ minutes remaining.
Anthony, on the other hand, seemed to run out of gas at the end. He made only one of five shots in the final period, totaling just five points.