Before the ceremony, he revealed the anxiety he felt showing the tennis stars the film for the first time.
Coming-of-age drama CODA, about the only hearing member of a deaf family, has won the Screen Actors Guild's top award.
Will Smith was also among the big winners for his portrayal of Venus and Serena Williams's father in King Richard, winning best actor.
Before the ceremony, he revealed the anxiety he felt showing the tennis stars the film for the first time.