The victory also saw Del Potro book his place at next month's ATP World Tour Finals in London.
"Always when you beat the number one player of the world, you feel something special in your mind, feelings," the ATP's official website quotes Del Potro as saying.
"It's one moment so good to explain with words. I'm so happy, so excited to enjoy a little bit of this match."
Del Potro is only the fifth player to defeat Nadal on tour this year.