The champagne-fueled ceremony honored the best of film and television selected by a new group of 300 entertainment journalists from around the world, part of reforms made after a diversity and ethics scandal among Globe voters.
Downey was named best supporting actor in a movie for portraying the professional nemesis of J. Robert Oppenheimer in director Christopher Nolan's drama about the making of the atomic bomb. The movie was one of last year's biggest box office hits.
"A sweeping story about the ethical dilemma of nuclear weapons grosses one billion dollars. Does that track?" Downey joked before thanking Nolan and the team behind the film.
Randolph won the Globe for supporting actress in a movie for her role of a grieving mother in "The Holdovers." She said she was grateful for the chance to portray the "beautiful and flawed woman."
"Barbie," the summer blockbuster starring Margot Robbie as the iconic doll, led all nominees going into the ceremony with nine nods. Robbie appeared at the ceremony in a hot pink gown and boa, a replica of the outfit worn by 1977's superstar Barbie doll.
The Globes kicked off Hollywood's annual awards season, which culminates with the Oscars on March 10, and brought top stars together after six months of strikes by actors and writers in 2023.
Jo Koy, a comedian hosting his first major awards show, opened the ceremony with jabs at some of the A-list stars and their projects.
"Oppenheimer," a historical drama running three hours long, "needed another hour," Koy joked. "I felt like it needed some more back story."
The ceremony was broadcast live on CBS and streamed simultaneously for subscribers to Paramount+ with Showtime PARA.O.
Pop superstar Taylor Swift joined the Hollywood crowd in a shiny, green gown. The singer was a nominee for "Taylor Swift: The Eras Tour," her concert film that was in the running in a new category for cinematic and box office achievement.
In the television field, "Succession" was expected to win accolades for its final season about the high-stakes battle for control of a global media empire. It led all nominees with nine nods, followed by restaurant dramedy "The Bear" with five.
There were 27 first-time nominees for this year's Globes.
Known as a boozy celebration more relaxed than the Oscars, the Globes nearly became extinct. A 2021 Los Angeles Times report revealed ethical lapses and a lack of diversity among the roughly 80 members of the Hollywood Foreign Press Association, the group that previously voted on the Globes. The 2022 ceremony was scrapped while the organization made reforms.
Last year, the Globes were sold to new owners and the association was disbanded. Eldridge Industries and Dick Clark Productions now operate the awards, with a voting body of 300 journalists from 75 countries with 60% racial and ethnic diversity.
