The 20-year-old An defeated Acosta Bermoy of Cuba in the final in a match that went into overtime. An won in the final minutes with a decisive throw that landed Bermoy on her back.
An won silver at the Beijing Games four years ago.
Earlier in the day, An knocked out top-seeded Misato Nakamura in the second round.
The bronze medals were won by Italy's Rosalba Forciniti and France's Priscilla Gneto.