The former Doctor Who star said she had become more passionate than she thought possible about performing for a live audience, as she picked up the award for her role in Yerma on Sunday.
The 34-year-old broke down in tears as she accepted the award at London’s Royal Albert Hall, beating competition from the likes of double Academy Award winner and former Labour MP Glenda Jackson.
Speaking after picking up her award, she told the Press Association: “Probably theatre, I am so passionate about it and I never knew what it would do for me personally and professionally.
The mother-of-two dedicated her award to her sons, even though she admitted it would mean nothing to them yet.
“Everything I do, I do it for them,” she added.
The Olivier for best actor went to Jamie Parker, who plays Harry Potter in the West End box office smash hit Harry Potter And The Cursed Child.