Memphis scored the game's final seven points to erase Philadelphia's lead with less than 2 minutes left, sending the Sixers to their eighth straight loss.
JaMychal Green had 13 points and 10 rebounds, including a pair of free throws with 4 seconds left to seal the Grizzlies' fourth straight win and 10th in the last 13.
Ersan Ilyasova had season bests of 23 points and 17 rebounds for Philadelphia. Dario Saric scored 17 points, while Nik Stauskas added 12 points, despite missing seven of his eight shots from outside the arc.
The Sixers led 91-89 with 1:57 remaining, but Zach Randolph, who had 12 points and 14 rebounds, scored inside and Memphis made enough free throws in the closing minutes.
Injuries and rest left the 76ers with only nine players dressed.
Memphis has become adept at pulling out close games. The victory was the Grizzlies' 11th straight that either went to OT or was decided by five points or fewer.
And the experience showed after Saric scored inside to give Philadelphia its 91-89 lead. That's when turnover problems plagued the Sixers, allowing Memphis to pull away.
Philadelphia committed 16 turnovers and was 13 of 26 from the foul line.
