Memphis, who will face the winner of San Antonio and Golden State in the conference final, almost blew a 12-point lead with three minutes left but hung on to win the series 4-1 and bring an end to the postseason for last season's conference champions.
Zach Randolph had 28 points and 14 rebounds for the Grizzlies, who lost the opener before winning four straight in a series in which all five games were decided by six points or less.
In Game Five on Wednesday, hosts Oklahoma City trailed 80-68 with three minutes to go but clawed their way back and had a chance to tie the game but Kevin Durant missed a jump shot in the last seconds to seal the Thunder's fate.
Durant finished with 21 points, eight rebounds and six assists but made just five of 21 from the field.
Serge Ibaka added 17 for top seeds Oklahoma City, who lost All Star Russell Westbrook earlier in the playoffs.
Mike Conley had 13 points and 11 assists while Marc Gasol got 10 and three blocks for the Grizzlies.
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