The Texans looked like the side more likely to score in the first quarter as Ryan Fitzpatrick moved the ball well downfield, connecting with Arian Foster and Andre Johnson, but they were unable to put points on the board.
Washington took the lead in the second quarter when Robert Griffin III moved his side downfield and handed the ball off to full-back Darrel Young on the goalline, and he powered in for the score. However, they did miss the extra point.
Houston responded immediately as Fitzpatrick threw his first touchdown pass of the season to DeAndre Hopkins in a deep throw down the right sideline, and the receiver beat DeAngelo Hall for a 74-yard score.
It got better for the visitors when a punt was blocked by Alfred Blue and the running back ran the ball for the five-yard score to give his side an eight-point lead.
The Redskins tried to get back on track in the second half, but were prevented from getting a foothold in the match as JJ Watt dominated the offensive line and brought down Griffin for a sack.
The Texans managed to hold firm in the fourth quarter and put together a scoring drive to seal the victory as Randy Bullock nailed a 42-yard field goal.