British star Mark Rylance picked up a best supporting actor Oscar on a night dominated by the row over the lack of black nominees.
Rylance, who beat off competition from Sylvester Stallone, Mark Ruffalo and fellow Brits Christian Bale and Tom Hardy, won the gong for his role in Bridge Of Spies.
In his acceptance speech, he took a swipe at politicians, praising the leadership of the movie's director Steven Spielberg, who he said was "unlike some of the leaders we are being presented with".
Host Chris Rock opened the 88th Academy Awards ceremony by declaring Hollywood is "racist" and admitting he considered boycotting the ceremony because of the absence of black nominees.
The comedian, who welcomed the audience in the Dolby Theatre to the "white People's Choice Awards", cracked a series of jokes about the race issue and added the controversy over police shootings of black suspects in the US to his targets.
He said: "Everyone wants to know is Hollywood racist? You have to go at it the right way. Is it burning-cross racist? Fetch-me-some-lemonade racist? No. It's a different kind of racist.
"Is Hollywood racist? You're damn right it's racist but it's sorority racist."
He added: "That's how Hollywood is but things are changing."
Alicia Vikander won the first big award of the night, picking up the best supporting actress Oscar for her role in The Danish Girl.
The Swedish-born actress, who stars alongside Eddie Redmayne in the film, said: "Eddie, thank you for being the best acting partner.
"I could never have done it without you."
Other notable British successes included Amy, the British-made film about the late Amy Winehouse, which won the Oscar for best documentary feature film.
The first British success went to Jenny Beavan, who won best costume design Oscar for Mad Max: Fury Road.
Ms Beavan, who was famously described as a 'bag lady' by Stephen Fry at the Baftas, said: "I want to say one quite serious thing, but it could be horribly prophetic, Mad Max, if we are not kinder to each other and if we don't stop polluting our atmosphere."
Asked backstage about her choice of Oscars outfit, Beavan said: "I am very happy to talk about it. I don't do frocks and absolutely don't do heels, I have a bad back.
"I look ridiculous in a beautiful gown. This was a homage to Mad Max and I obviously didn't get it quite right at the Baftas, the scarf was meant to be an oil rag."
Gesturing to her fake leather jacket, she added: "This is Marks & Spencer with Swarovski at the back, I had a bit of a shoe malfunction and the glitter fell off. I just like feeling comfortable and as far as I'm concerned I'm really dressed up."
Mad Max: Fury Road also won the Oscar for best production design and a clutch of other technical awards.
The first Oscar of the evening went to Spotlight, the story of how the Boston Globe newspaper exposed abuse by Roman Catholic clergy. The film picked up the best original screenplay gong, which was collected by co-writers Tom McCarthy, who also directed the film, and Josh Singer.
Speaking backstage, McCarthy said: "It's electric, it's really exciting. With a project like this, you don't think about awards. It's truly thrilling and rewarding."
When an electrical extension cord fell down from the ceiling above their heads as they spoke to reporters, McCarthy quipped: "That was the Catholic Church."
The Big Short writer McKay urged people not to vote for candidates that take money from "banks, big oil and weirdo billionaires" in the upcoming American election, but said he didn't have someone in mind.
Clutching her Oscar backstage, Vikander said she hoped The Danish Girl, about transgender artist Lili Elbe, opens up opportunities for more films about transgender stories.
She said: "I definitely hope so. I came on this film only two years ago and know it wasn't an easy film to get made, to see the cultural change since I finished the film with Caitlyn Jenner and Transparent and Tangerine, it's a social change and in the way this film has been so educational for me, I hope it can open up a wider conversation."
TV star Kevin Hart introduced singer The Weeknd who performed his Oscar-nominated song, Earned It, from Fifty Shades Of Grey.
Hart addressed the diversity issue plaguing this year's awards, saying he wanted to take a minute to "applaud my fellow actors and actresses of colour who didn't get nominated tonight.
"Let's not let the negative issue of diversity beat us. Congratulations on an amazing year."