The Spurs held a 12-point advantage late in regulation but allowed the Grizzlies to stage a 14-2 run in the final 2 minutes to force extra time before eventually pulling out a seventh straight win over Memphis.
Tim Duncan pumped in 24 points and grabbed 17 rebounds.
Marco Belinelli added 19 points and Kawhi Leonard helped out with 17 for the Spurs.
The Grizzlies' Mike Conley erupted for 30 points, including nine during their late surge.
Zach Randolph contributed 17 points and eight rebounds.