Boston chose to play defense for the entirety of the 24-second shot clock and that strategy worked when Cleveland's Shaun Livingston misfired on a jump shot with 8 seconds to go.
After taking a time out, the Celtics got the ball to Green and he came through with the winning basket that dealt Cleveland its sixth straight loss.
Boston rallied from a 14-point deficit with 8 minutes to go. Brandon Bass produced a season-best 22 points and Green had 21. Pierce just missed a triple-double while scoring 19 points, seizing 10 rebounds and dishing out eight assists.
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