Oklahoma City had also been trying to win six in a row, but suffered its second home loss of the campaign.
The Thunder owned a 10-point lead at the start of the second period, but by halftime the Grizzlies had moved in front 56-45. Oklahoma City came no closer than six points during the second half.
Gay scored 28 points and Randolph had 20 points and 11 rebounds before being ejected with 2:05 to play. Randolph has produced a double-double in all seven games this season.
The six straight Memphis wins have followed a season-opening loss on the road to the Los Angeles Clippers.
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