Published: 2018-03-05 09:34:22 BdST
It is the first Oscar for the 49-year-old Rockwell, a veteran of independent films such as "Moon," "Seven Psychopaths" and "The Way Way Back."
"I'd like to thank the Academy," an ecstatic Rockwell said as he accepted the award. "Never thought I'd say those words."
Rockwell was seen as a favourite for the Academy Award after winning Golden Globe, Screen Actors Guild and BAFTA awards earlier this year.
In "Three Billboards," from Twenty-First Century Fox Inc's Fox Searchlight, Rockwell plays an officer named Dixon who clashes with a mother whose daughter was killed in their small Midwestern town. The mother, Mildred, believes the authorities are not doing enough to investigate her daughter's death.
Rockwell is the son of two actors and appeared in his first independent film while he was in high school.
On stage, Rockwell described a time when he was 8 years old and his father pulled him out of class to go to the movies.
"My mom and dad's love of movies became my love of movies," he said. "So thank you for that mom and dad. I love you."
He was praised for his portrayal of Dixon as a complex man forced to face humility. But the character drew criticism from some filmgoers who felt he was unfairly redeemed despite his racist views.
Asked about the controversy on Sunday, Rockwell described "Three Billboards" as a "dark fairy tale." If it were a true-life story, both Dixon and Mildred likely would have gone to prison, he said.
"It's not like they are all of a sudden redeemed at the end of the movie," Rockwell told reporters backstage. "They have a lot of work to do, and maybe some therapy."