Houston (7-6-5) had not won since beating D.C. United 4-0 on May 8. Philadelphia (7-6-6) saw its five-game unbeaten streak snapped, dropping its first game since losing 5-3 at Montreal on May 25.
Clark's goal also put an end to Houston's franchise record 388-minute scoreless streak when he headed in Jermaine Taylor's cross from the left sideline from 8 yards out.
Houston had not scored since Warren Creavalle's goal at Columbus on June 1.
Philadelphia's best chance came before halftime when Houston goalkeeper Tally Hall stopped Aaron Wheeler's shot from the left box and Conor Casey's rebound attempt went high.