The actress picked up the award for her role as Paulina in "The Winter's Tale" at the ceremony at London's Royal Opera House, and her win means she has now been honoured more than anyone else since the awards, which recognise excellence in theatre, began 40 years ago.
But the 81-year-old star joked she was "livid" to have won, as it meant she had lost a bet with her grandson.
"Ladies and gentlemen, I'm absolutely livid as I had a bet with my grandson... And I'm never going to be able to forget it."
"Gypsy" was the big winner with four prizes, including best actress in a musical and best supporting actress in a musical for Imelda Staunton and Lara Pulver respectively, as well as best musical revival and best lighting design.
In celebration of the ceremony's 40th anniversary, the finale saw 15 past Olivier winners, including Maria Friedman, Ruthie Henshall and Jill Halfpenny, perform "What I Did for Love", which features in the first-ever Best New Musical winner, "A Chorus Line".
