Houston climbed back to the .500 mark by beating a team from the Western Conference for the first time this season.
The Rockets led by as many as 21 points in the third quarter only to see New Orleans battle back to within two when Greivis Vasquez hit a 3-pointer with 1:49 to play.
New Orleans then missed its final three shots and a jumper from Houston's Chandler Parsons with 65 seconds left accounted for the final score.
Harden made 10-of-20 shots from the field and 9-of-11 from the foul line in reaching the 30-point mark for the third time in eight games this year. Omer Asik added 15 points and 12 rebounds for the Rockets and both Parsons and Marcus Morris had 13 points.
Vasquez scored 25 for the Hornets. Ryan Anderson contributed 20 points and 12 rebounds off the bench.