The Rockets ended a three-game losing streak, the most recent of those setbacks having come with Harden out of action with his ankle injury.
He returned from a one-game absence to hit 10-of-20 shots from the field and all nine of his attempts from the foul line.
Houston led by as many as 10 points in the third period, but had to hold off the Wizards down the stretch. A 3-pointer by Chandler Parsons with 1:15 to play put the Rockets back in front by nine.
Parsons scored 11 of his 18 points in the fourth period. Houston guard Jeremy Lin, who produced a 38-point effort that equaled a career best in his previous outing against San Antonio, settled for 10 points on Wednesday.
Washington had gone 3-3 in his last six games after starting the season with an 0-12 mark. Bradley Beal paced the Wizards with 20 points.