The 22-year-old singer saw off tough competition from music titans - Taylor Swift, SZA, Miley Cyrus, Lana Del Rey, Jon Batiste, Dua Lipa and Olivia Rodrigo - to claim the top prize.
After picking up the award, which honours songwriting, a shocked Eilish said: "Wow, oops, yikes, oh my god. Damn that's stupid!"
She praised her fellow nominees as "incredible people, incredible artists, incredible music".
Eilish also thanked the director of the Barbie blockbuster Greta Gerwig for "making the best movie of the year", with the video cutting over to show Swift nodding in agreement.
And thanked the Recording Academy and her brother and fellow collaborator Finneas O'Connell, who she described as her best friend.
Mariah Carey presents the award for best pop solo performance to Miley Cyrus. (AP PHOTO)
Cyrus picked up two awards for her empowerment anthem Flowers, which was named record of the year, and for best solo pop performance.
While Victoria Monet was named the best new artist.
Cyrus was handed one of her gold trophies by Mariah Carey and said she almost missed the awards after getting stuck in traffic.
Monet, 34, thanked her single mother who was raising a "really bad girl".
"I just want to say to everybody who has a dream, I want you to look at this as an example.
"This award was a 15-year pursuit, I moved to LA in 2009 and I like to liken myself to a plant who was been planted, you can look at the music industry as soil, dirty or a source of nutrients.
"My roots have been growing underneath for so long, I feel like today I am sprouting," she said.
Hosting for a fourth time, comedian Trevor Noah opened the show by joking that it was "the only concert that starts on time."
In one of the night's first performances, country singer Luke Combs joined with Tracy Chapman for a duet of Fast Car, the hit song that she released in 1988 and that Combs remade into a massive country hit last year. Taylor Swift, Jelly Roll and other nominees stood in the audience and swayed to the music.
Swift, the 34-year-old in the middle of the world's highest-grossing tour, was competing for an unprecedented fourth album of the year trophy with Midnights.
No other artist in the 66-year Grammys history has claimed the coveted honour four times. Music legends Frank Sinatra, Paul Simon and Stevie Wonder won three each.
She faced competition from a female-led field that included SZA, the most-nominated artist of the night, and indie rock band boygenius, a band formed by indie rock stars Phoebe Bridgers, Lucy Dacus and Julien Baker.
Earlier Kylie Minogue won best pop dance recording for Padam Padam - her first Grammy win in 18 years.
The 55-year-old Australian singer was not present to collect the gong, but the song's British producer Peter Rycroft appeared on stage.
Kylie Minogue won the best pop dance recording Grammy for Padam Padam. (AP PHOTO)
"This is such a unique process on this song, it started as an idea with a friend who I wrote it with originally and we built up a fairly rough demo and it got into the hands of Kylie," he explained.
"She is such a powerhouse, she recorded her own vocals in her hotel room and sent me the project - she is very hands on and very collaborative."
Women figure prominently in the 2024 Grammys field. Just one man, Jon Batiste, made the cut among eight nominees for the album prize. Other contenders include Olivia Rodrigo and Lana Del Rey.
Music from the blockbuster Barbie movie received 11 nominations.
Contenders in the best new artist field included rapper Ice Spice, country singer Jelly Roll, R&B and pop singer Victoria Monet, singer-songwriter Coco Jones and folk-pop singer Noah Kahan.
With PA
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