The TV premiere of Behind the Candelabra, starring Michael Douglas as flamboyant pianist Liberace and Matt Damon as Scott Thorson, was seen by 2.4 million people in the US.
The Nielsen Company said it was the HBO network’s biggest audience for one of its original movies since medical drama Something the Lord Made in 2004.
A further 1.1 million people tuned in for a repeat of the film that aired immediately after Sunday’s premiere.
Behind the Candelabra, Steven Soderbergh’s film, will be released in UK cinemas on June 7.
Based on Scott Thorson’s memoir Behind the Candelabra: My Life with Liberace, the film charts the life of the American pianist and the secret affair he had with the author, played by Matt Damon.
The drama received its world premiere at the Cannes Film Festival earlier this month.
ABC’s Dancing With the Stars remains the most-watched programme on US television with around 15 million viewers last week.