For the third year in a row, the South Korean band won best pop group and best pop song for their chart-topping dance anthem, Butter.
"This whole thing is a miracle," said singer RM. "Seriously, we'll never take this for granted."
Taylor Swift took home the award for best female pop artist for the sixth time, as well as best pop album for her album Evermore.
Swift's overall number of American Music Awards now stands at 34, increasing her lead as the artist with the most awards. With 26 wins, Michael Jackson is in second position.
In 2019, she was also named artist of the decade.
The diva described Evermore, which won best pop album at the Grammys in March, as the "adventurous, fun younger sister" to her lockdown album Folklore, which won album of the year.
"I'm so lucky to be in your life and to get to have you in mine," the celebrity said, thanking fans for their support.
Unlike most award events, the American Music Awards' winners are determined solely by fan votes.