Her victories tied her with Beyonce as the most wins by a woman in one evening.
"Mom, gold is good!" Adele shouted as she took the album of the year trophy.
The night's other big winners were Grohl's Foo Fighters, who won five awards. They noted that they made their album "Wasting Light" in a garage.
"To me this award means a lot because it shows that the human element of making music is what's most important. Singing into a microphone, learning to play an instrument and learning to do your craft, that's the most important thing for people to do," Grohl said as the band accepted their best rock performance trophy for "Walk." "It's not about being perfect. It's not about sounding absolutely correct. It's not about what goes on in a computer. It's about what goes on in here (your heart) and what goes on here (your head). ... Long live rock `n' roll!"
Chris Brown, Paul McCartney, Katy Perry, Nicki Minaj and Bruce Springsteen were among the performers.
But the evening's most moving moment came from Jennifer Hudson, who paid tribute to Whitney Houston, who was found dead in the bathtub of her hotel room at the Beverly Hilton on Saturday.
It is often said that the show must go on, and although difficult, the Grammys were no exception.
The show started off on a somber note, as host LL Cool J appeared in black, and told the audience: "There is no way around this. We've had a death in our family."
He then led the audience in prayer to "our fallen sister."
The show also marked the first time Rihanna and Brown have appeared at the same awards show since his attack on her three years ago, which also occurred on the eve of the Grammys. The event forced both to drop out of the show and led to an assault conviction for Brown. While Brown's career took a major hit, he did see a comeback in 2011. Meanwhile, Rihanna was up for album of the year.
Brown won best R&B album: "First and foremost, I gotta thank God, and thank the Grammys for letting me get on this stage and do my thing," he said "All my fans, I love you. We got one. Thank you."
Justin Vernon, whose band Bon Iver beat Nicki Minaj, The Band Perry, J. Cole and Skrillex for best new artist, accepted the award with mixed emotions.
The Associated Press contributed to this report.