The Celtics snapped a two-game skid and ended the Thunder's winning streak at three. It was the first of two road games in as many nights for Oklahoma City, which will take on Philadelphia Saturday.
Boston overcame a seven-point deficit after one period, but held only a two-point lead with 3 minutes to go in the third quarter. The Celtics closed the quarter on an 11-1 run with Green scoring seven of those points.
The Boston lead grew to as many as 14 points in the fourth period.
Paul Pierce led the Celtics with 27 points. He made all seven of his foul shots and Boston went 21-of-24 as a team.
Kevin Garnett added 18 points and nine rebounds while Green had 17. Boston went 9-of-17 from 3-point range while Oklahoma City was only 6-of-24.