She took home the prize for her portrayal of the Queen in The Audience.
Dame Helen, a previous Oscar-winner for The Queen, accepted the award saying: “Your Majesty, you did it again.”
Other British wins included Alex Sharp for best actor and Marianne Elliott for best directing of The Curious Incident of the Dog in the Night-Time, which was also named best play.
The stage adaptation of the hit novel started life at the National Theatre in London before transferring to Broadway.
Dame Helen, who beat off competition from fellow British actresses Carey Mulligan and Ruth Wilson, dedicated the award to her husband, director Taylor Hackford.
Her co-star Richard McCabe, who plays prime minister Harold Wilson, also received the honour for best featured actor in a play.
Alex Sharp said it felt “insane” to be awarded the prize for best actor
London-born Alex Sharp, who plays a gifted mathematician with Asperger’s syndrome in The Curious Incident, beat Bradley Cooper and Bill Nighy for the best lead actor award.
As well as best director, Marianne Elliott’s Broadway transfer of the play was also honoured with awards for best lighting and best scenic design.
When she was nominated in April, Elliott had told the BBC: “We had no idea when we first started how the hell this play was going to go down. We had no idea whether there’d be an audience for it. So to see it go to Broadway is quite amazing.”
An American in Paris and Fun Home took most awards in the musical categories.
An American in Paris won four technical awards, while Fun Home won for best score, book and direction.