A weeping Quan, who was born in Vietnam, kissed his Oscar trophy as he held it on stage.
"My journey started on a boat. I spent a year in a refugee camp. Somehow I ended up here on Hollywood's biggest stage," Quan said.
"They say stories like this only happen in the movies. I cannot believe it's happening to me. This is the American dream."
Quan was among the early winners at the Oscars. Guillermo del Toro's "Pinocchio" was named best animated feature.
A crisis response team was on hand in case of an unexpected twist. The group was formed after Will Smith smacked Chris Rock on stage last year, tarnishing the film industry's most prestigious ceremony.
Host Jimmy Kimmel, who landed on the Dolby Theater stage by parachute in a tribute to best picture nominee "Top Gun: Maverick," joked in his opening monologue about the audience reaction to Smith's attack last year.
"If anything unpredictable or violent happens at the ceremony, just do what you did last year - nothing," he told the crowd of A-list celebrities. "Maybe give the assailant a hug."
The 95th Academy Awards ceremony was broadcast live on Walt Disney Co's (DIS.N) ABC network. The Academy of Motion Picture Arts and Sciences hoped to move past the slap and stage a glitzy show and boost sagging TV ratings.
Ahead of the awards, nominees dressed in designer gowns and tuxedos touted their movies on a champagne carpet in place of the traditional red.
Producers said they planned to celebrate the moviegoing rebound of the past year, one that some feared might never happen when streaming took hold during the Covid-19 pandemic.
Several of 2022's biggest hits at the multiplex landed in the best picture race, from "Top Gun: Maverick" and "Everything Everywhere Everywhere All at Once" to "Elvis" and "Avatar: The Way of Water."
Last year, the television audience for the Academy Awards ranked as the second-lowest ever with 16.6 million viewers.
The big films on Sunday's ballot, rather than some of the little-seen movies nominated in recent years, could help draw more viewers. The musical performances also may boost viewership.
Lady Gaga emerged as a last-minute addition and was expected to sing her nominated "Top Gun" song "Hold My Hand." Oscars producers said last week that Gaga was unable to make it because she was in the middle of filming a sequel to the 2019 movie "Joker."
Pop superstar Rihanna also will take the stage, performing "Lift Me Up" from "Black Panther: Wakanda Forever."
Michelle Yeoh faces off in the best actress category with Cate Blanchett, who played a devious orchestra conductor in "Tar." Best actor may be a toss-up between "Elvis" star Austin Butler and Brendan Fraser, who played a severely obese man in "The Whale."
Winners are voted on by the roughly 10,000 actors, producers, directors and film craftspeople who make up the film academy.