Hip-hop duo Macklemore and Ryan Lewis took four awards – best new artist plus best rap album, song and performance.
Justin Timberlake won three, while New Zealand teenager Lorde picked up two including song of the year for Royals.
Paul McCartney was among the other double winners and also reunited with his Beatles bandmate Ringo Starr.
The pair teamed up for Paul McCartney’s song Queenie Eye during the ceremony, which is known for its heavyweight on-stage collaborations.
The show was opened by Jay-Z and his wife Beyonce, while Madonna joined Macklemore and Ryan Lewis during their anti-homophobia anthem Same Love, as 33 couples got married on stage.
Other collaborations included Metallica performing with pianist Lang Lang and Daft Punk, Nile Rodgers and Pharrell Williams being joined by Stevie Wonder to perform Get Lucky.
Get Lucky, which featured producer and singer Pharrell Williams and disco guitarist and producer Nile Rodgers, was one of the biggest hits of 2013.
As well as scooping album and record of the year, Daft Punk won best pop duo/group performance for Get Lucky and best dance/electronica album for Random Access Memories.
The album was also named best engineered album, non-classical, which was credited to its engineers.
The French dance pioneers, real names Thomas Bangalter and Guy-Manuel de Homem-Christo, never appear in public without their trademark robot helmets.
As well as performing, Paul McCartney picked up the trophies for best music film and best rock song for Cut Me Some Slack, a collaboration with the surviving members of Nirvana.
It beat The Rolling Stones’ Doom And Gloom, from their 50th anniversary album GRRR!, as well as tracks by veteran metal band Black Sabbath, stadium rockers Muse and singer-guitarist Gary Clark Jr.
Black Sabbath did scoop best metal performance, while Led Zeppelin won best rock album for their live recording Celebration Day.
Rapper Macklemore and producer Ryan Lewis, who found fame after self-releasing their album The Heist, won four awards from seven nominations.
Seventeen-year-old Lorde’s debut single Royals earned song of the year and best pop solo performance after catapulting her to the top of the charts around the world last year.
Jay-Z started the night with the most nominations, up for nine awards. He won best rap/sung collaboration for Holy Grail, featuring Justin Timberlake.
Justin Timberlake, Pharrell Williams and rapper Kendrick Lamar were among the acts who went into the ceremony with seven nominations.
Other winners included Adele for her James Bond theme Skyfall, which won the prize for best song written for visual media, and Scottish percussionist Evelyn Glennie, who won best classical instrumental solo.
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