Jrue Holliday added 13 points and a career-high 15 assists for Philadelphia, which shot 51 percent from the field. Richardson had 14 of his 22 points in the final period, and Turner was 10 of 15 from the field for the game.
Philadelphia (10-6) had 54 points in the paint, most of those in the first half. Thaddeus Young had 15 points and Lavoy Allen contributed 10 points and 10 rebounds.
Ben Gordon led Charlotte with 19 points, and rookie Jeffery Taylor matched a career-high with 16 points.
The Bobcats (7-8) have dropped three straight and four of five to fall below .500.
Charlotte trailed most of the second half until Ramon Sessions' hustle play tied it at 81 with 9:17 left to play.
Sessions ran after a long rebound near the top of the key and tipped it over a 76ers player so he could grab it on his way up the court. He gathered the ball and drove to the basket. He missed the layup but grabbed the rebound before landing and put it back in, bringing the crowd to its feet.
But that's when Richardson began to heat up, hitting three 3-pointers to help push Philadelphia's lead to 95-87 with 3:55 left in the game.
Charlotte made one last run to pull within four with 1:11 left, and Richardson responded with a 3-pointer from the left corner to seal the victory.
The 76ers held a 54-50 lead after a tight first half that featured 15 lead changes.
Philadelphia pounded the ball inside and Young and Allen proved difficult to stop, combining for 21 points in the first half.
Gordon, who was 7-of-10 shooting from 3-point range and finished with 26 points in Wednesday's loss to Atlanta, picked up right where he left off. He made three first-half 3-pointers and led the Bobcats with 15 points at the break.
Kemba Walker finished with 13 points and nine rebounds for the Bobcats but had a reduced role, playing only 27 minutes. Walker had played more minutes than anyone on the team.
Holliday took Walker to the post a few times and Bobcats coach Mike Dunlap quickly made a move to go with Sessions.
Michael Kidd-Gilchrist, the No. 2 overall pick in the draft, had 10 points and eight rebounds for the Bobcats.