Green hit 13-of-19 shots from the field and his 3-pointer with 45 seconds remaining boosted Boston in front by five points.
Boston halted a two-game skid and its win, combined with a loss by Philadelphia, put the Celtics in the post-season for the sixth straight year. Only one playoff spot remains in the Eastern Conference and Milwaukee has all but wrapped up that one.
Detroit was led by 24 points and 17 rebounds from Greg Monroe. It was the fourth loss for the Pistons in five games.
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