It follows her win at the Golden Globes earlier this month. Her co-star John Lithgow, who plays Winston Churchill in the Netflix series, was overlooked at the Globes but won best actor at last night’s SAG awards.
However The Crown was beaten to the ensemble cast prize by fellow Netflix show Stranger Things.
The sci-fi programme, set in the Eighties, stars Winona Ryder and a young cast led by British star Millie Bobby Brown.
Downton Abbey, which ended in December 2015, also missed out on the prize, its final chance for a SAG award.
At the ceremony in Los Angeles, Foy paid tribute to another co-star, Matt Smith, who played Prince Philip.
“Thank you for making this job a joy and making me laugh,” she said. It was one of the few acceptance speeches that did not criticise Donald Trump.
In the battle for best actor, Denzel Washington, star of Fences, beat Manchester By The Sea’s Casey Affleck. Emma Stone was named best actress for La La Land.
The cast of Hidden Figures were the surprise winners of the best ensemble prize, beating Manchester By The Sea and Moonlight after La La Land missed out on a nomination.
Viola Davis won best supporting actress for her performance opposite Washington in Fences, while Mahershala Ali was named best supporting actor for his role in coming-of-age drama Moonlight.
Bryan Cranston won the award for best actor in a limited series or TV movie for his portrayal of former US president Lyndon B Johnson in HBO film All The Way.
Dolly Parton presented her co-star from Nine To Five, Lily Tomlin, with the SAG Life Achievement Award.
She told the audience: “Don’t be anxious about missing an opportunity. Behind every failure is an opportunity someone wishes they had missed.”
|Winners: John Lithgow and Claire Foy both won awards for The Crown Jordan Strauss/Invision/AP|
Now they're Hollywood royalty! The Crown's Claire Foy and John Lithgow win top acting prizes at SAG Awards... as she declares her 'love' for co-star Matt Smith in acceptance speech
Claire Foy and John Lithgow were honoured by their contemporaries at Sunday night's Screen Actor's Guild Awards for their show-stopping turns in The Crown.
Hot off her Golden Globe win for portraying the young Queen Elizabeth II, Claire scooped the Outstanding Performance by a Female Actor in a Drama Series in Los Angeles on Sunday.
Foy, 32, was still flustered as she took hold of her statuette following the win by her American co-star John Lithgow, 71, for his portrayal of Prime Minister Winston Churchill in the drama created by Peter Morgan.
Lithgow was honoured with the Outstanding Performance by a Male Actor in a Drama Series after losing out in the Best Supporting Actor – Series, Limited Series or Television Film category at the Golden Globes.
In her acceptance speech, Claire thanked her friend and co-star Matt Smith, who plays Prince Philip, telling him she loved him.
'Thank you for making this job a joy and making me laugh,' she told the audience.
The pair had arrived together for the ceremony posing for photos on the red carpet.
While The Crown lost out to Netflix stable mate Stranger Things for the best ensemble in a TV series, Foy and Lithgow's wins were warmly greeted by their co-stars.
The Shrek star acknowledged on stage that he would never have thought of casting himself as Churchill.
He thanked the 'magnificent cast of about 50 wonderful English actors' saying 'these are the people who have delivered me up to this platform.'
And backstage he gushed about Foy, saying she was the main reason he decided to accept the role.
'Claire was in the first sentence I heard about this project. I said 'yes' when I heard Claire. I have many actor friends in London who have worked with Claire and the word ‘lovely’ keeps coming up,' the 71-year-old said.
While she may have picked up some of the most prestigious awards in the film industry, Claire revealed before the ceremony the unusual place she likes to store her trophies.
Speaking before the event, she said: 'In my toilet, not actually in my toilet but in my downstairs toilet.
'You can't put it anywhere noticeable, because everyone would be like, 'Oh yeah, showing off".'
The British reigned supreme with SAG nominations, and ensured they turned out in force at the annual ceremony.
UK-made shows The Crown,Downton Abbey and Game of Thrones all battled it out for Outstanding Performance by an Ensemble in a Drama Series.
The trio went up against Netflix hit Stranger Things, for which English child actress Millie Bobby Brown was nominated, and controversial series Westworld.
GoT also bagged nods for Peter Dinklage for his turn as Tyrion Lannister and won the Outstanding Performance by a Stunt Ensemble in a Television Series category.