The movie's 25-year-old star, Mikey Madison, was named best actress and the film earned best director for Sean Baker and trophies for original screenplay and editing.
Anora was made for $US6 million ($A9.7 million), a tiny sum by Hollywood standards.
It emerged as the winner in an unpredictable Oscars race that included papal thriller Conclave, Jewish immigrant story The Brutalist and blockbuster musical Wicked.
"If you're trying to make independent films, please keep doing it. We need more. This is proof," said Baker, a director known for making small films about porn stars, transgender prostitutes and other marginalised people.
Madison scored an upset over Demi Moore, who had been favoured to win best actress for her role in The Substance.
"I grew up in Los Angeles, but Hollywood always felt so far away from me," Madison said on stage.
"To be here standing in this room today is really incredible."
She said she wanted to "thank and honour the sex worker community", adding, "I will continue to be an ally."
Anora, released by independent distributor Neon, has generated $US40 million at global box offices.
Wicked, by comparison, has hauled in $US728 million.
Adrien Brody claimed his second Oscar, winning best actor for his role as a Jewish immigrant and architect who chases the American dream in The Brutalist.
His first win came 20 years ago for The Pianist, when he was 29.
"Acting is a very fragile profession," Brody said.
"No matter where you are in your career, it can all go away. I think what makes this most special is the awareness of that."
Zoe Saldana was named best supporting actress for her role as the fixer for a Mexican drug lord in Emilia Perez, a Spanish-language musical released on Netflix.
The movie, which also won best original song for El Mal, was a favourite for best picture earlier this year.
Its chances dwindled when offensive social media posts surfaced from star Karla Sofia Gascon.
The actor, the first openly transgender person nominated for an acting Oscar, disappeared from the awards circuit but attended Sunday's ceremony.
Kieran Culkin received the best supporting actor award for A Real Pain, in which he plays one of two cousins who travel to Poland to study their family's roots, beating Australian Guy Pearce for his role in The Brutalist.
Culkin thanked his wife and mother of his two children, Jazz Charton, and said he had recently told her he wanted a total of four kids.
Culkin said she joked she would agree if he won an Oscar.
"Let's get cracking on those kids!" Culkin said to his wife from the stage.
Other Australians nominated included writer and director Adam Elliot and producer Liz Kearney for the animated feature Memoir of a Snail, while cinematographer Greig Fraser was nominated for his work on Dune: Part Two.
Winners are chosen by the roughly 11,000 actors, producers, directors and film craftspeople who make up the Academy of Motion Picture Arts and Sciences
No Other Land, a film showing Palestinian West Bank resistance to Israeli soldiers tearing down their homes and evicting residents to create a military training ground, won the documentary feature film Oscar on Sunday.
The prize for best animated feature went to independent film Flow, the first movie from Latvia to win an Oscar.
Brazilian movie I'm Still Here received the best international feature award.
Nominees Ariana Grande and Cynthia Erivo opened the Oscars celebration with a Wizard of Oz-themed medley including the show-stopping hit Defying Gravity from their film Wicked.
Midway through the show, host Conan O'Brien brought a group of Los Angeles firefighters to the stage and thanked them for their work during the January wildfires.
He also invited them to deliver a few jokes.
"It's great to be back with Conan," Pasadena Fire Captain Jodi Slicker said.
"Usually when he calls, he's stuck in a tree."
