The surprising victory ended a six-game road losing streak for the 76ers. Memphis brought a 12-2 home mark into the contest.
Richard missed the contest with a lower back strain and Wright took advantage of the playing time to make 8-of-11 shots from the field and 7-of-8 from the line.
Philadelphia played the second contest in an eight-game road trip that began with a loss to Brooklyn.
Spencer Hawes added 20 points and nine rebounds for the 76ers, who hit 52 percent of their field goal attempts and were 9-of-16 from beyond the arc.
Zach Randolph led Memphis with 23 points. The Grizzlies were within two points with 10:30 to play, but Philadelphia went on a 13-0 run to seize control.