Martin converted a three-point play and a 3-pointer as the Thunder scored nine of the first 11 points of the fourth quarter, prompting Memphis coach Lionel Hollins to call a timeout with the lead down to 75-73 with 10:08 left.
Randolph banked in a jumper to stabilize the Grizzlies, and Prince followed with a 3-pointer from the right corner to push the lead back to seven.
Durant then sandwiched a pair of driving buckets around Derek Fisher's 3-pointer as Oklahoma City pieced together seven consecutive points to tie it at 84 with 3:47 to play.
The Grizzlies went back up 90-87 when Serge Ibaka missed one of two free throws and Gasol followed with a hook shot with 1:08 to go.
It was a competitive new chapter in an increasingly fierce rivalry, but there weren't any scuffles between the two teams this time. They had combined for nine technical fouls in three meetings during the regular season, including one confrontation that got Randolph and Kendrick Perkins ejected.
It ended up being almost dead even in several key categories: Oklahoma City had two more rebounds (43-41), four more points in the paint (36-32) and two fewer turnovers (12-10). Each team scored only four second-chance points.
Notes: Durant finished second in the MVP voting behind LeBron James. He got 93 of the 121 second-place votes in the balloting announced Sunday. … The Thunder made their first nine shots in their only win of the season against Memphis, the best start to a game by an NBA team this season. They missed their first 10 in this one. … Nick Collison was called for a flagrant foul after leveling Prince on a baseline drive in the second quarter.