The 76ers made up a 10-point deficit in the fourth period, forced overtime when James Anderson hit a 3-pointer with six seconds to go in regulation and went on to end a two-game skid.
The Rockets' Francisco Garcia failed to draw iron with a 3-point try and Philadelphia expanded its lead to five on Anderson's two foul shots. That gave the 76ers enough of a cushion to withstand a 3-pointer by Jeremy Lin with eight seconds to go.
Anderson, averaging 6.9 points a game in his eight previous appearances this season, broke loose with 36 points to help the 76ers overcome a 34-point show from Lin that included nine 3-pointers.
Turner added 23 points and the 76ers also picked up 18 each from Spencer Hawes and Tony Wroten.
Houston played without star guard James Harden, who is suffering from a sore foot.