There were also posthumous awards for Leonard Cohen and Carrie Fisher at the ceremony
R&B star Bruno Mars was the biggest winner of the 60th Grammys, winning all the six awards he was nominated.
He won record of the year for his party anthem 24K Magic, and album of the year for the album of the same name.
Mars dedicated his award to songwriters, saying: "Thank you guys so much... first off to the other nominees in this category - Lorde, Kung-fu Kenny (Kendrick Lamar), Jay-Z, Gambino - you guys are the reason I'm in the studio pulling my hair out man, 'cos I know you guys are only going to come with the top-shelf artistry and music and thank you guys for blessing the world with your music, I mean that."
It was also a strong night for Lamar, who walked away with five awards.
Ed Sheeran won the best pop vocal album award for his record Divide, but was not available to collect the honour in person.
Awards were also posthumously given to Leonard Cohen, for best rock performance, and Carrie Fisher, for best spoken word album with her reading of her memoir The Princess Diarist.
During the awards ceremony, Lady Gaga, Rita Ora, Cardi B, Kelly Clarkson and Sam Smith were among the stars who wore or held a symbolic flower to show support for the anti-sexual harassment MeToo and Time's Up campaigns.
Lady Gaga wore white rosebuds and a Time's Up pin on the shoulder of her black Armani outfit, and whispered "Time's Up" during her performance of ballads Joanne and Million Reasons.
Kelly Clarkson, who was carrying her white rose, talked about its symbolism, saying that to her, it reflects "hope and peace and sympathy and resistance".
Songwriter Diane Warren showed up with white gloves, with one word on each hand: "Girl" and "Power".
Sam Smith, who performed at the ceremony at Madison Square Garden in New York City, said: "I hope we keep striving forward for equality for absolutely everyone."
Elton John performed with a white rose on top of his piano.
While on the red carpet, Sting spoke about Time's Up and MeToo, saying it was "an important conversation" and "a time of learning and hopefully, eventually, a time of healing".
Hillary Clinton, meanwhile, joined celebrities including John Legend, Cher, Cardi B and Snoop Dogg to mock Donald Trump in a parody sketch that saw them read excerpts from Michael Wolffs's controversial book Fire And Fury.
The book - dismissed by Mr Trump as full of lies - depicts a chaotic White House, a President who was ill-prepared to win the office in 2016, and aides who scorned his abilities.
Mrs Clinton, the former Democratic presidential candidate who lost the 2016 election to Mr Trump, was the last of the famous faces to appear in the video, in which Grammys host James Corden pretended to be auditioning the celebrities as contenders for a spoken word award.
On the hunt for a GRAMMY Award of his own, James Corden auditions celebrities for the spoken word version of Michael Wolff's "Fire and Fury." pic.twitter.com/SjTobAbv2N— The Late Late Show with James Corden (@latelateshow) January 29, 2018