Durant's key pull-up jumper capped a fourth-quarter surge than saw the Thunder star score 12 points down the stretch, rallying his team from a 12-point second-half deficit.
He finished with 35 points, 15 rebounds and six assists while Kevin Martin came off the bench to pop in 25 points for the second straight game as Thunder opened up a 1-0 lead in their Western Conference semifinal series.
Reggie Jackson also reached double figures with 12 points for the victors.
Marc Gasol paced the Grizzlies with 20 points and 10 rebounds but turned the ball over before Durant's go-ahead basket.
Zach Randolph added 18 points with 10 boards in the loss.
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