After losing seven straight, the Rockets have won two out of three.
Harden made all 12 of his free throws and was backed up by 18 points and 12 rebounds from Patrick Patterson.
Carlos Delfino made 4-of-6 attempts from 3-point range and scored 14 points for Houston.
New Orleans lost its second in a row after winning seven of nine. Eric Gordon paced the Hornets with 20 points and Ryan Anderson had 19. New Orleans made just 38 percent of its field goal shots and was 3-of-20 from beyond the arc.