Moore won best female actor in a musical or comedy film for her leading role in "The Substance," the story of a fading actress seeking a fountain of youth.
"I'm just in shock right now," Moore said as she held her trophy on stage. "I've been doing this a long time, over 45 years. This is the first time I've ever won anything as an actor."
A few years ago, Moore said, she thought her career might be over. When she read the script for "The Substance," "the universe told me you are not done," she said.
Stan was named best male actor in a film musical or comedy for "A Different Man," a movie about a man with facial disfigurement.
"Our ignorance and discomfort around disability and disfigurement has to end now," Stan said. "We have to normalize it and continue to expose ourselves to it and our children."
Zoe Saldana appeared overwhelmed when she was named best supporting film actress for playing a lawyer who helps a Mexican drug lord start a new life and transition to a woman in musical thriller "Emilia Perez."
"My heart is full of gratitude to the Golden Globes for celebrating our film," Saldana said on stage as she wept through her speech and thanked her co-stars and director.
Kieran Culkin was named best supporting film actor for "A Real Pain," a dramedy about cousins who travel to Poland to explore their family's roots.
At the start of the show, first-time host Nikki Glaser welcomed the celebrity crowd to "Ozempic's biggest night" and teased Timothee Chalamet, Harrison Ford, Selena Gomez and other power players in the audience.
"You could do anything, except tell the country who to vote for," Glaser said, referring to widespread Hollywood support for the losing candidate in the recent U.S. presidential election.
On the red carpet ahead of the show, celebrities shined in black, gold and silver gowns with an occasional red or periwinkle in the mix. "Wicked" star Ariana Grande wore a yellow Givenchy gown with a beaded bodice that she said was a tribute to the yellow brick road leading to Oz in the movie musical.
"It's so exciting to be here because I'm such a fan of every single person I bump into," Grande said of the star-studded crowd in Beverly Hills.
Winning a Globe can shine a spotlight on movies and performances in the run-up to the Academy Awards in March. So far, awards pundits say, there is no clear favorite for the coveted best picture prize at the Oscars.
Globe honorees were chosen by 334 entertainment journalists from 85 countries, compared with roughly 9,000 voters who select the Academy Awards. The Globes voting body has been expanded in recent years and organizers instituted reforms after being criticized for ethical lapses and a lack of diversity.