Visiting quarterback Jalen Hurts had a poor first half but finished with 234 yards through the air and two touchdowns in southern Texas.
The scores were locked at 14-14 at half-time, before Philadelphia safety CJ Gardner-Johnson picked off a career-high and league-leading fifth interception which got the ball back to Hurts.
The Houston-born signal-caller then tossed a 17-yard touchdown pass to AJ Brown that gave the Eagles the lead.
The Texans hit back with a field goal before Hurts threw another scoring pass in the final quarter, this time to tight end Dallas Goedert, that he added to with a two-point conversion run.
The Eagles' defence stepped up again to seal the victory as cornerback James Bradberry scooped up an attempted-touchdown pass by Houson second-year quarterback Davis Mills.