The television premiere of Behind the Candelabra, starring Michael Douglas as flamboyant pianist Liberace, 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.
Steven Soderbergh's film is released in UK cinemas on 7 June.
Based on Scott Thorson's memoir Behind the Candelabra: My Life with Liberace, it 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.
The dance competition, America's version of the BBC's Strictly Come Dancing, had around 15 million viewers last week.