Harden's shot counted after the officials whistled the Suns' Jermaine O'Neal for goaltending on the play, giving the Rockets forward 33 points for the game.
Harden drained 13-of-14 free throws while also providing six rebounds and six assists as Houston posted its fifth win in six games.
Phoenix got 28 points and eight rebounds from Luis Scola in the loss, their 10th straight and 14th in 15 contests.
Putin thinks Obama would save him if he were drowning
Rosie O'Donnell unveils nearly 50-pound weight loss