Gaga, now a nine-time Grammy victor, won best pop solo performance for "Joanne", while hit "Shallow", from "A Star is Born", was named best song written for visual media. "I'm in tears with honor and gratitude..." she tweeted after her win for A Star Is Born was announced.
At almost the two-hour point of the show, country duo Dan + Shay seemed ebullient when they announced Drake's name as victor for best rap song.
Obama, who got a rousing applause from the crowd, so much so that she had to pause saying her lines and restart once it calmed, said music "fueled" her through the last decade.
Gaga also won the award for Best Pop Solo Performance for the live version of "Joanne".More news: Orange warning in effect as Erik brings 120km/h gusts
Hugh Jackman, an Emmy and Tony victor, won his first Grammy, picking up best compilation soundtrack for visual media for "The Greatest Showman". "Thank you for being my island", she said. Cardi B's "Invasion of Privacy", Kacey Musgraves' "Golden Hour", Brandi Carlile's "By the Way, I Forgive You" and H.E.R.'s self-titled album are also in contention.
Women artists scored nominations in all of the top categories, after being largely muted a year ago: Gaga, Carlile, rapper Cardi B and pop futurist Janelle Monae are among the frontrunners.
Cuban-born Camila Cabello kicked off the televised show with a dance heavy performance of her hit single "Havana" with Latin artists J Balvin, Ricky Martin and Young Thug. "Bradley, I loved singing this song with you".
When asked about the lack of women in the top categories at the 2018 Grammys, Recording Academy CEO Neil Portnow said women need to "step up". And, well, let's just say there aren't a lot of "who is Drake" and "who is Kendrick Lamar" articles being written for tonight. But it was female artists who dominated nominations in the top categories. Yolanda Adams, Fantasia and Andra Day will honor the late Aretha Franklin with a performance.