Its voters granted a whopping seven awards to the film, which was made for around $25 million and became independent studio A24's biggest-ever hit, with a global box office gross above $100 million.
"This is too many. We're so lucky!" said co-director Daniel Scheinert, collecting the night's final prize.
Michelle Yeoh won best lead performance, and Stephanie Hsu won best breakthrough performance.
It is the first year in which the Film Independent Spirit Awards have opted for gender-neutral acting categories.
"Michelle, you beat a bunch of men!" yelled Jamie Lee Curtis in the backstage press room.
Curtis was the film's only nominee who failed to win -- losing best supporting performance to her co-star Ke Huy Quan.
Scheinert and Daniel Kwan won director and best screenplay, and the film also won best editing.
The absurdist sci-fi comedy stars Yeoh as the matriarch of a Chinese-American laundromat-owning family, who end up fighting a universe-hopping supervillain while undergoing a tax audit.
"You believed in us. You believed in the masterpiece from the Daniels," said Yeoh, addressing the studio's producers.
"My boys, thank you for writing such an incredible script that gave us the opportunity to be here, to be seen, to be heard."
'So humbling and so cool'
This year's Spirit Awards were held the weekend before the Oscars. Voting for the season-concluding Academy Awards is currently under way.
Final Oscars voting closes on Tuesday, before Hollywood's most coveted golden statuettes are handed out at a glitzy ceremony next Sunday.
Among the films that could receive a late Oscars boost from their Spirit Award wins Saturday were best documentary "All the Beauty and the Bloodshed," best first feature "Aftersun," and best cinematography winner "Tar."
"Women Talking" received the pre-announced Robert Altman Award, which honors a film's director, casting director and overall cast.
But in a repeat of scenes at recent high-profile prizegiving ceremonies from Hollywood's actors', producers' and directors' guilds, the night's big winner was "Everything Everywhere," which cemented its already clear Academy Award frontrunner status.
"It's been so humbling and so cool," producer Jonathan Wang told AFP on Saturday's red carpet.
The movie -- which features characters with hot dog fingers, sex toy-shaped trophies and talking rocks -- has overcome predictions from some pundits that it would prove too bizarre for mainstream audiences and voters.
It leads the nominations at the Oscars, with 11 nods.
"What's happened is a lot of people went out and they gave our movie a chance," said Wang.
"They said 'let's watch it for what it is' and they got past the kind of things that were going to be 'too edgy' for them. And then they were bulldozed by the emotion of it.
"That's what we wanted to do. So that's the highest compliment -- that we were able to actually do that."