Starring Taraji P. Henson, Octavia Spencer and Janelle Monae, it took the trophy for outstanding performance by a cast in a motion picture, the SAG equivalent of a best film Academy Award.
Theodore Melfi's movie, which recounts the story of African-American mathematicians who helped NASA put the first men in space, was a shock winner, with Kenneth Lonergan's "Manchester by the Sea" widely tipped for the top prize.
It also beat coming-of-age drama "Moonlight," comedy "Captain Fantastic" and race relations story "Fences."
"Manchester" star Casey Affleck -- the frontrunner for the best actor Oscar -- was also shut out, with the SAG award going instead to Denzel Washington for "Fences."
Washington, 62, who has two Oscars, also beat competition from Andrew Garfield ("Hacksaw Ridge"), Viggo Mortensen ("Captain Fantastic") and Ryan Gosling ("La La Land").
In the best actress category, Emma Stone won for "La La Land," Damien Chazelle's whimsical tribute to the musicals of Hollywood's golden age.
The support acting awards went to Mahershala Ali for "Moonlight" -- his second trophy of the night after the "Hidden Figures" cast prize -- and Viola Davis, who made it a double for "Fences."
Ali, 42 -- best known for his portrayal of White House chief of staff Remy Danton in Netflix political drama "House of Cards" -- gave an emotional speech about the need to support the marginalized.
"I think what I've learnt from working on 'Moonlight' is we see what happens when we persecute people -- they fold into themselves," said Ali, a Muslim with a Christian minister for a mother, fighting back tears.
