James Anderson, who finished the night with a career-high 36 points, hit a three-pointer with 6.6 seconds remaining in regulation to help send the game into overtime.
Key stops by Philadelphia's defense and clutch free throws by Thaddeus Young (15 points and eight rebounds) and Evan Turner (23 points, seven rebounds and five assists) helped the 76ers pull away late and secure the 123-117 OT victory.
Tony Wroten had his first career triple-double of 18 points, 10 rebounds and 11 assists. His desperation heave from midcourt nearly won it for Philadelphia at the buzzer.
Rookie Michael Carter-Williams of the 76ers and James Harden of the Rockets both sat out of this game with foot-related injuries.
Jeremy Lin led the Rockets with 34 points, including a franchise-record nine three-pointers. Dwight Howard had 23 points, while Chandler Parsons chipped in 22 of his own.
Defense was once again a huge issue, as the Rockets gave up another 100-plus points to the opposition for the sixth time this season.
Houston will play the second game of an Atlantic Division back-to-back tomorrow night at Madison Square Garden against the New York Knicks, while Philadelphia will visit Atlanta on Friday to do battle with the Hawks.