The group fun. took home best new artist, in something of an upset over Frank Ocean, and song of the year for "We Are Young," featuring Janelle Monae.
Ocean didn't win in the major categories, but took home two trophies, including best urban contemporary album.
Other big winners included Gotye, who took home three awards, including record of the year for "Somebody That I Used To Know."
Mumford & Sons also won big, taking home the top prize of album of the year for "Babel."
Taylor Swift opened the show with her song, "We Are Never Ever Getting Back Together."
The Associated Press contributed to this report.