The Rockets limited the Warriors to 12 points in the first period while taking a 19-point lead and went on to end a two-game slide.
Harden scored 34 points, the third time in four games he has reached the 30-point mark. Howard had 18 rebounds to go with his 22 points.
Houston held Golden State to 35 percent shooting and the Warriors made just 2-of-16 from beyond the 3-point arc.
Stephen Curry led Golden State with 22 points, but he hit only 5-of-14 shots.