The world's top-ranked player dominated the final match against He Bingjiao of China to win her first Olympic gold medal.
An's 2-0 victory (21-13, 21-16) also ended Korea's 28-year gold medal drought in the sport's singles event, since Bang Soo-hyun's gold in 1996.
A day earlier, Spanish favorite Carolina Marín, the 2016 Olympic women's singles champion, was forced to retire in tears due to a traumatic knee injury in the semifinals.
As of Monday, Korea now has 11 gold, eight silver, and seven bronze medals overall. In the gold medal count, Korea ranks fifth, following China, the U.S., France, and Australia.