The French electronic music act also won the prize for Best Pop Duo/Group Performance, as well as the Record of the Year statuette for "Get Lucky," featuring Pharrell Williams, and the Best Dance Album honor.
Although Daft Punk stars Guy-Manuel de Homem-Christo and Thomas Bangalter remained in their signature costumes and helmets throughout the ceremony, they hugged each other upon hearing they won the evening's top prize of Album of the Year and silently collected their statuettes, while their collaborator, famed 1970s singer-songwriter Paul Williams, gave a heartfelt acceptance speech in which he joked about finally kicking his addictions to drugs and alcohol only to work with robots, a reference to Daft Punk's unique appearances.
Lorde won the Grammy for Best Pop Solo Performance, while her hit "Royals" was named Song of the Year.
The Best New Artist prize went to Macklemore & Ryan Lewis.
The duo also picked up the trophies for Best Rap Performance and Best Rap Song for "Thrift Shop," and the Best Rap Album honor for "The Heist."
They took the stage again late in the show and performed their song "Same Love," while musician-actress Queen Latifah officiated the weddings of 33 gay and straight couples who agreed to wed on the air.
"This song is not a love song for some of us, but for all of us," Queen Latifah told the crowd.
Madonna, who is also a vocal gay-rights activist, made a special guest appearance during the segment and sang part of her 1980s hit "Open Your Heart to Me."
Married superstars Beyonce and Jay Z kicked off the ceremony at the Staples Center with a performance of her hit "Drunk in Love." LL Cool J served as host of the event.