"There's no other way to describe it. It's the moment of a lifetime," Bigelow said. "It's so extraordinary to be in the company of my fellow nominees, such powerful filmmakers, who have inspired me and I have admired, some of them for decades."
Among those Bigelow and "The Hurt Locker" beat are ex-husband James Cameron and his sci-fi spectacle "Avatar." Bigelow and Cameron were married from 1989-91.
Cameron was seated right behind Bigelow at the Oscars and joined a standing ovation for her, clapping vigorously and saying, "Yes, yes" after she won.
First-time winners took all four acting prizes: Sandra Bullock as best actress for "The Blind Side"; Jeff Bridges as best actor for "Crazy Heart"; Mo'Nique as supporting actress for "Precious"; and Christoph Waltz as supporting actor for "Inglourious Basterds."
The Oscar marks a career peak for Bridges, a beloved Hollywood veteran who had been nominated four times in the previous 38 years without winning. Bridges, who played a boozy country singer trying to clean up his act, held his Oscar aloft and thanked his late parents, actor Lloyd Bridges and poet Dorothy Bridges.
"Thank you, Mom and Dad, for turning me on to such a groovy profession," said Bridges, recalling how his mother would get her children to entertain at parties and his father would sit on the bed teaching him the basics of acting for an early he landed on his dad's TV show "Sea Hunt."
"I feel an extension of them. This is honoring them as much as it is me," Bridges said.
Bullock, an industry darling who had never before been nominated, won for her role as a wealthy woman who takes in homeless future NFL star Michael Oher, who was living on the streets as a teen.
The award wraps up a wild year for Bullock, who had box-office smashes with "Blind Side" and "The Proposal" and a flop with "All About Steve," which earned her the worst-actress trophy at the Razzies the night before the Oscars.
"Did I really earn this or did I just wear you all down?" Bullock asked the Oscar crowd. Bullock gushed with praise for her fellow nominees, including Meryl Streep, who she joked is "such a good kisser."
The supporting-acting winners capped remarkable years, Mo'Nique startling fans with dramatic depths previously unsuspected in the actress known for lowbrow comedy and the Austrian-born Waltz leaping to fame with his first big Hollywood role.
"I would like to thank the academy for showing that it can be about the performance and not the politics," said Mo'Nique, who plays the heartless, abusive welfare mother of an illiterate teen in the Harlem drama "Precious: Based on the Novel `Push' by Sapphire."
Mo'Nique added her gratitude to the first black actress to win an Oscar, Hattie McDaniel, the 1939 supporting-actress winner for "Gone With the Wind."
"I want to thank Miss Hattie McDaniel for enduring all that she had to so that I would not have to," she said, adding thanks to Oprah Winfrey and Tyler Perry, who signed on as executive producers to spread the word on "Precious" after it premiered at last year's Sundance Film Festival.
"Precious" also won the adapted-screenplay Oscar for Geoffrey Fletcher.
"This is for everybody who works on a dream every day. Precious boys and girls everywhere," Fletcher said.
Waltz's award was presented by last season's supporting-actress winner, Penelope Cruz, who gave Waltz a kiss as he took the stage. "Oscar and Penelope. That's an uber-bingo," Waltz said.
Though a veteran stage and TV actor in Europe, Waltz had been a virtual unknown in Hollywood before Quentin Tarantino cast him as the prattling, ruthless Jew-hunter Hans Landa in his World War II saga.
"Quentin with his unorthodox methods of navigation, this fearless explorer, took this ship across and brought it in with flying colors, and that's why I'm here," Waltz said. "This is your welcoming embrace, and there's no way I can ever thank you enough."
"Avatar" won three Oscars, for visual effects, art direction and cinematography, beating "The Hurt Locker" for the latter. "The Hurt Locker" also won out over "Avatar" for film editing, sound editing and sound mixing.
With nine nominations each, "The Hurt Locker" and "Avatar" came in tied for the Oscar lead.
"Hurt Locker" screenwriter Mark Boal, who won the Oscar for original screenplay, thanked Bigelow, calling her an "extraordinary and visionary filmmaker," and dedicated his Oscar win to the troops still in Iraq and Afghanistan, along with those who did not make it home. Boal also affectionately recalled his father, who died a month ago.
Missing from the onstage celebration for the "Hurt Locker" win was producer Nicolas Chartier, who was banned by the academy from attending the Oscars because of e-mails he sent urging members to vote for his movie -- an academy violation.
"Up" earned the third-straight feature-animation Oscar for Disney's Pixar Animation, which now has won five of the nine awards since the Academy of Motion Picture Arts and Sciences added the category.
The film features Ed Asner providing the voice of a crabby widower who flies off on a grand adventure by lashing thousands of helium balloons to his house.
"Never did I dream that making a flip-book out of my third-grade math book would lead to this," said "Up" director Pete Docter, whose film also won for best musical score.
Pixar has a likely contender in the wings for next Oscar season with this summer's "Toy Story 3," reuniting voice stars Tom Hanks and Tim Allen.
Argentina's "The Secret in Their Eyes" pulled off a surprise win for foreign-language film over higher-profile entries that included Germany's "The White Ribbon" and France's "A Prophet."
"Crazy Heart" also won for original song with its theme tune "The Weary Kind."
The song category typically comes late in the show, after live performances of the nominees that have been spaced throughout the ceremony. Oscar producers tossed out those live performances this time in favor of montages featuring the songs and footage from the films they accompany.
"The Cove," an investigation into grisly dolphin-fishing operations in Japan, was picked as best documentary.
Oscar hosts Steve Martin and Alec Baldwin opened the show with playful ribbing of nominees. They also made note of Oscar organizers' decision to double the best-picture category from five films to 10.
"When that was announced, all of us in Hollywood thought the same thing. What's five times two?" Martin said.
Leaders of the Academy widened the best-picture category from the usual five films to expand the range of contenders for a ceremony whose predictability had turned it into a humdrum affair for TV audiences.
Oscar ratings fell to an all-time low two years ago and rebounded just a bit last year, when the show's overseers freshened things up with lively production numbers and new ways of presenting some awards.
The overhaul continued this season with a show that farmed out time-consuming lifetime-achievement honors to a separate event last fall and hired Martin and Baldwin as the first dual Oscar hosts in 23 years.