Film drama Nomadland has scooped three Oscars including best picture, while British stars Sir Anthony Hopkins and Daniel Kaluuya have won acting awards.
Nomadland's Chloé Zhao made history as the first non-white woman and second woman overall to win best director.
At 83, Sir Anthony is the oldest ever recipient of best actor; while best supporting actor Kaluuya is the first black British actor to win an Oscar.
"I did not expect to get this," said Sir Anthony, who missed the ceremony.
British actress-turned-writer/director Emerald Fennell also won a screenplay award.
The star, who plays Camilla Parker Bowles in The Crown, won best original screenplay for Promising Young Woman, which she also directed.
Frances McDormand won best actress for her role in Nomadland, while veteran South Korean actress Yuh-Jung Youn won best supporting actress for Minari.
The trophies were handed out in one of the grand halls at Los Angeles's stylish Union Station to allow for a Covid-safe ceremony, while many UK-based nominees were at a venue in London - although Sir Anthony was at neither.
Absent Sir Anthony beats Boseman
Sir Anthony won best actor for his masterful performance as a man suffering with dementia in The Father, 29 years after he won his first Oscar for The Silence of the Lambs.
His victory was the biggest surprise of the night. The award had been tipped to go to the late Chadwick Boseman, who died aged 43 last August, for Ma Rainey's Black Bottom.
Sir Anthony was neither in LA nor at the British Film Institute in London, the ceremony's UK venue, so instead posted a message on Instagram on Monday morning.
"At 83 years of age I did not expect to get this award, I really didn't," he said in a video filmed in his "homeland" of Wales. "I'm very grateful to the Academy, and thank you."
Sir Anthony went on to pay tribute to Boseman, whom he said had been "taken from us far too early", and said he felt "very privileged and honoured".
The Father, which will be released in the UK on 11 June, also won best adapted screenplay for Sir Christopher Hampton and director Florian Zeller, who called Sir Anthony "the greatest living actor".
Big night for Nomadland
The slow-burning drama about a woman living in her van in the American West after the financial crash won the top prize for best film, plus best director and best actress.
McDormand, who now has three best actress Oscars, is one of the only professional performers in the film. Most of the rest of the cast is made up of real people playing fictionalised versions of themselves.
In her acceptance speech, Zhao thanked the real-life nomads "for teaching us the power of resilience and hope".
Before Zhao, the only woman to have won the directing prize in the Oscars' 92-year history was Kathryn Bigelow for The Hurt Locker in 2010.
McDormand spoke of her hopes for the revival of big-screen cinema, asking viewers: "One day very, very soon, take everyone you know into a theatre, shoulder to shoulder in that dark space and watch every film that's represented here tonight."
She then said: "We give this one to our Wolf," and howled like a wolf - a tribute to the film's sound mixer Michael Wolf Snyder, who took his own life at the age of 35 last month.
Meanwhile, black-and-white film Mank, which led the nominations with 10, picked up two awards, as did Sound of Metal, Judas and the Black Messiah, Ma Rainey's Black Bottom and Soul.
Victorious Kaluuya 'happy to be alive'
The 32-year-old Londoner won best supporting actor for his incendiary performance as Black Panthers leader Fred Hampton in Judas and the Black Messiah.
"What a man. How blessed we are that we live in a lifetime where he existed," the actor said. "I am humbled to be nominated for portraying a man whose principles I deeply respect and for guiding me to walk in his footsteps."
Kaluuya also paid tribute to his mother, who was watching at the BFI, who he said "gave me my factory settings so I can stand at my fullest height".
But she could be seen asking "What is he talking about?" when her excited son told the global audience of millions: "My mum met my dad, they had sex, it's amazing. I'm here. I'm so happy to be alive so I'm going to celebrate that tonight."
Yuh-Jung Youn became the first South Korean actress to win an Oscar, for her role as the grandmother in Korean-American family drama Minari.
She beat Olivia Colman, Amanda Seyfried, Maria Bakalova and Glenn Close to the prize for best supporting actress. It was Close's eighth nomination without a win. Youn told the crowd she "doesn't believe in competition" and paid tribute to her fellow nominee, asking: "How can I win over Glenn Close?"
From Call the Midwife to the Oscars
The night's other British winners included Emerald Fennell for her first film as writer and director.
Until now, Fennell has been best-known for appearing in front of the camera, playing Patsy in BBC drama Call the Midwife and Camilla Parker-Bowles in Netflix's The Crown.
Her satirical thriller stars Carey Mulligan as a woman avenging the rape of her best friend. In her speech, Fennell recalled how they shot it in 23 days while she was heavily pregnant.
She thanked her family, including her young son, "who did not arrive until a couple of weeks after shooting, thank God, because I was crossing my legs the whole way through".
She is the first British woman to win the best original screenplay award since it was established in its current form in 1958.
The other UK winners included Sir Christopher Hampton, who shared the best adapted screenplay award with Florian Zeller for The Father; and Atticus Ross, who shared the best score prize with Trent Reznor and Jon Batiste for Soul.
Fellow Brits Andrew Jackson and Andrew Lockley won best visual effects for Tenet; James Reed won best documentary feature for My Octopus Teacher; and Martin Desmond Roe won best live action short for Two Distant Strangers, which addresses the police killings of black people in the US.
Mia Neal and Jamika Wilson became the first black winners of the best make-up and hairstyling award, triumphing for their work on Ma Rainey's Black Bottom. They shared the award with Spaniard Sergio Lopez-Rivera.
In an impassioned acceptance speech, Neal said: "Jamika and I break this glass ceiling with so much excitement for the future because I can picture black trans women standing up here and Asian sisters and Latinx sisters, and one day it won't be unusual and groundbreaking, it will just be normal."
The film also won best costume design for 89-year-old Ann Roth, making her the oldest woman to win an Oscar.
A very different Oscars
The ceremony was delayed by two months and was inevitably different this year. At Union Station, nominees walked an unusually sparse red carpet before sitting, spaced out but mostly maskless, in one of the station's converted halls.
Like last year, there was no single host, so the show was introduced by director and Oscar-winning actress Regina King, who began on a political note.
Referring to the conviction of former police officer Derek Chauvin of the murder of George Floyd, she said: "If things had gone any different in Minneapolis I might have traded in my heels for marching boots."
Most nominees and winners were there in person, but some were in London, while others appeared by satellite from locations including Paris, Prague and Sydney.