The Sixers have lost an NBA-record 28 consecutive games dating to last season and at 0-18 matched the New Jersey Nets' start in 2009-10.
Mike Conley led the Grizzlies with 20 points, while Matt Barnes and Jeff Green finished with 13 apiece as Memphis won for the seventh time in the last nine.
Isaiah Canaan led the Sixers with 16 points, while Robert Covington and Hollis Thompson scored 12 points apiece. Jerami Grant finished with 11 points.
The Sixers led 76-71 with 7:38 remaining and Memphis fans were booing their team. But the Grizzlies went on a 15-1 run to retake control of the game, with Randolph scoring eight points in the rally.