The film stars Mortensen as Tony "Lip" Vallelonga, a racist Italian-American bouncer enlisted by Shirley, a black concert pianist, to drive him on a tour of the Deep South in 1962.
"You get nervous up there", he said.
The film also sparked controversy months ago when relatives of the pianist at the centre of the story, Don Shirley, complained his depiction in the movie contained inaccuracies.
When he collected the trophy for "Moonlight", Ali was the first Muslim to win an Oscar for acting.
Mahershala Ali and wife Amatus Sami-Karim as they arrive at the 2019 Academy Awards on Sunday (February 24) at the Dolby Theatre in Los Angeles. "He told me, 'If you're going to tell the story, tell it from your father, me".
Ali took the stage, where he first thanked the man he portrayed, saying, "Trying to capture Dr. Shirley's essence pushed me to my ends, which is a reflection of the person that he was and the life that he lived, and I thank him".
He always knew it was a compelling tale. "This has been a long time coming", Carter said before thanking Lee (who was in the audience) for giving her her start in the business and dedicating the win to her 97-year-old mother watching in MA.
"I'm snakebit. Every time someone is driving somebody, I lose", Lee told reporters in response to a question about his reaction to the win for "Green Book". They were among the very few women directors nominated in a year with many feature-length contenders and just as many overlooked.
"I can't believe they have John Lewis introducing Green Book", filmmaker Nia DaCosta tweeted.
It truly caps off a unusual journey in this year's Oscars.
While he had potential to be a star on the college court, Ali ultimately made it big in Hollywood earning his second Oscar on Sunday night.
Not only that but during the acceptance speeches for Best Picture, Shirley himself was never thanked, nor was the man who created the actual Green Book. Accepting the original screenplay award for the film, co-writer Farrelly thanked "the entire state of Rhode Island", among many others.