Downey, who was nominated for an Oscar in 1993 before his career was derailed by drug use, was named best supporting actor for his role as the professional nemesis of physicist J. Robert Oppenheimer.
"I'd like to thank my terrible childhood and the Academy, in that order," Downey joked before he saluted his wife Susan, who he said found him as a "snarly rescue pet" and "loved him back to life."
Randolph won the best supporting actress trophy for playing a grieving mother and cafeteria worker in the comedy set in a New England boarding school. She shed tears as she accepted her award.
"For so long, I always wanted to be different, and now I realise I just need to be myself," she said. "I thank you for seeing me."
Da'Vine Joy Randolph won the best supporting actress Oscar for The Holdovers. (AP PHOTO)
Talk show host Jimmy Kimmel, hosting the show for the fourth time, opened the ceremony by complimenting, and taking jabs at, many of the nominees and their films.
The comedian praised Barbie, the pink-drenched doll adventure, for remaking a "plastic doll nobody even liked anymore" into a feminist icon.
Before the film, there was "a better chance of getting my wife to buy our daughter a pack of Marlboro Reds" than a Barbie, Kimmel said.
Kimmel said many of this year's movies were too long, particularly Martin Scorsese's three-and-a-half hour epic Killer of the Flower Moon about the murders of members of the Osage Nation in 1920s Oklahoma.
"In the time it takes you to watch it, you could drive to Oklahoma and solve the murders," he joked.
Meanwhile Britain's The Zone of Interest, about a German officer's family living next door to the Auschwitz extermination camp during World War II, collected the Oscar for best international feature film.
Mstyslav Chernov's 20 Days in Mariupol, a harrowing first-person account of the early days of Russia's invasion of Ukraine in 2022, won the best documentary Oscar.
Prior to the awards, hundreds of pro-Palestinian protesters angered by the Israel-Gaza conflict shouted and slowed traffic in the blocks surrounding the Dolby Theatre in Hollywood. "While you're watching, bombs are dropping," one sign read.
"The Oscars are happening down the road while people are being murdered, killed, bombed," said 38-year-old business owner Zinab Nassrou.
Protesters hold letters and symbols reading "Eyes on Rafah," during a demonstration in Los Angeles. (AP PHOTO)
Oppenheimer, the three-hour drama directed by Christopher Nolan, led the field with 13 nominations. The movie is the frontrunner to win the prestigious best picture prize, capping its sweep of other major awards this year.
"If the best picture isn't Oppenheimer, it will be one of the biggest upsets, if not the biggest upset, in the history of the Oscars," said Scott Feinberg, executive editor for awards at The Hollywood Reporter.
For Nolan, the night could bring his first directing Oscar, as well as the award for adapted screenplay. The director of The Dark Knight trilogy, Inception and other acclaimed films has never had a movie win best picture.
The ceremony may end with "the industry-wide coronation for Christopher Nolan," Feinberg said. With Oppenheimer, "he has he has made his best possible argument yet for why he is worthy of this recognition."
with Reuters
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