Parasite, the Korean language social satire about the wealth gap in South Korea, beat homegrown Hollywood movies with A-list casts The Irishman and Once Upon a Time in Hollywood to take the top prize of best movie ensemble cast on Sunday.
Winning the award, director Bong Joon Ho said it made him think that "maybe we haven't created such a bad movie."
"I am so honoured to receive this award. I will never forget such a beautiful night," he said through an interpreter.
Phoenix's terrifying performance as a loner who finds fame through violence in Joker has swept awards season.
"I am standing on the shoulders of my favourite actor - Heath Ledger," Phoenix said on Sunday, referring to the actor who won a posthumous Oscar in 2009 for his turn playing the comic book villain.
Zellweger, likewise, has picked up most of the prizes so far for her performance as a desperate, aging Judy Garland in biopic Judy.
"It was a difficult part," quipped Pitt of his role. "A guy who gets high, takes his shirt off and doesn't get on with his wife. It was a big stretch," he said to laughter, riffing on his own life as a twice-divorced Hollywood heartthrob.
DISAPPOINTING NIGHT FOR 'IRISHMAN'
Sexual harassment drama Bombshell went into Sunday's awards with a leading four nods but emerged empty-handed.
Martin Scorsese's Netflix gangster movie The Irishman had another disappointing night, despite a cast that includes Robert De Niro, Al Pacino, and Joe Pesci.
Several of the contenders for best picture at the Oscars on February 9 were not nominated for best movie cast ensemble at SAG.
Those left out include immersive World War 1 film 1917, the big winner at the Producers Guild Awards on Saturday, as well as dark comic book story Joker, heart-wrenching divorce drama Marriage Story, and novel adaptation Little Women.
De Niro, whose lead performance in The Irishman has been snubbed by the Oscars, Golden Globes and SAG, was given a lifetime achievement award at the SAG dinner and used his speech to take a veiled shot at US President Donald Trump.
Aniston, in her first television role since the end of Friends 25 years ago, seemed visibly shocked.
"What?! Oh my gosh. This is so unbelievable," she said.
Comedy The Marvelous Mrs Maisel and British royal drama The Crown took the prizes for their TV ensemble casts. But Mrs Maisel actress Alex Borstein said the comedy prize should have gone to quirky British comedy Fleabag.
Moments earlier, Fleabag creator Phoebe Waller-Bridge accepted the best television comedy actress statuette, capping a year of multiple awards for her and the show.
"This whole thing has been a dream and if I wake up tomorrow and find it's been just that, thank you. It's been the most beautiful dream," Waller-Bridge said.