Zach Randolph provided 23 points and 12 rebounds while Marc Gasol added 23 and 11 for the Grizzlies, who improved to 5-0 at home in the post-season and pushed the second-seeded Thunder to the brink of elimination in their Western Conference semifinal series.
Fifth-seeded Memphis rallied from a 17-point second-quarter deficit en route to the victory, their 19th in 20 home games overall.
The result put them one win away from the first conference final appearance in franchise history.
Kevin Durant supplied 27 points, seven rebounds and seven assists for the Thunder, who were held to 33 percent shooting from the field in the second half.
Kevin Martin added 18 points in the loss.