Daft Punk's "Random Access Memories" won album of the year and the group's hit, "Get Lucky," won record of the year. The French duo also picked up honors for best dance/electronica album for "Random Access Memories" and pop duo/group performance for "Get Lucky." The song also earned Williams one of his four trophies.
Macklemore & Ryan Lewis won best new artist and rap album for "The Heist," beating outing Kendrick Lamar, Jay Z, Kanye West and Drake.
"Wow, we're here on the stage right now," said Macklemore, thanking fans first, then his fiancee and team. "I want to say we made this album without a record label, we made it independently and we appreciate all the support."
Lorde was the princess of the Grammys. Her hit "Royals" won song of the year and best pop solo performance.
"Thank you everyone who has let this song explode because it's been mental," she said.
Macklemore & Ryan Lewis performed the gay-acceptance hit "Same Love," and 33 couples - some same-sex - got married in the middle in the performance as Queen Latifah officiated.
The 56th annual awards show was hosted again by LL Cool J.
The Associated Press contributed to this report.