Co-stars Fiennes and Okonedo won the Best Actor and the Natasha Richardson Award for Best Actress awards respectively for their performances as Antony and Cleopatra in the National Theatre production of Shakespeare's epic tragedy of the same name.
It marks the time in 30 years the lead acting awards have been presented to actors from the same production. The last time was in 1988, when Lindsay Duncan and Eric Porter received prizes for their performances in "Cat on a Hot Tin Roof".
"Harry Potter" star Fiennes, who previously won the Best Actor prize in 2016 for his roles in both "The Master Builder" and "Richard III", told London's Evening Standard: "I'm very emotional but I'm bottling it up. I love doing this play, I love this production, I love Sophie and Simon. It's been an amazing journey and I couldn't be happier. I'm happy to have this wonderful role really and just to get this is a cherry on the cake I suppose."
"I'm so overwhelmed, with Ralph winning first. It was too much for me," Sophie added. "It was really exciting. We've got to do a show on Wednesday and now we've got to live up to this!"
"The Inheritance" was named Best Play, while the London transfer of Lin-Manuel Miranda's Hamilton was named Best Musical. Rosalie Craig was given the Best Musical Performance award for her lead role in the gender-bending revival of Stephen Sondheim's Company, while Marianne Elliott was presented with the Milton Shulman Award for Best Director for the same production.
The Charles Wintour Award for Most Promising Playwright went to Natasha Gordon for "Nine Night", Hamilton's Jamael Westman won the Emerging Talent Award while theatre mogul Sir Cameron Mackintosh was honoured with the Lebedev Award.
The ceremony was presented by Phoebe-Waller Bridge at London's Theatre Royal, Drury Lane.