An audience in Chicago are said to have been "ecstatic" at seeing Harry Potter and the Sorcerer's Stone - as it is known in the US - on Thursday, according to the Daily Telegraph.
The much-anticipated movie version of JK Rowling's first best-selling book about the boy wizard goes on general release in both the US and UK on 16 November.
The film is schuduled to be released at two-and-a-half hours long, almost an hour longer than most children's films.
In comparison, Toy Story 2 was 92 minutes long and The Lion King 89 minutes.
The film will première in London under the British title Harry Potter and the Philosopher's Stone on 4 November.
Advance copies of the movie are yet to arrive in the UK where press previews are scheduled to begin the week following the première.
The screening in Chicago was reportedly a complete surprise to the invited audience, who were told only to expect a "family" film ahead of the main feature.
Christopher Columbus, the movie's director, is reported to have said afterwards: "The Harry Potter readers were ecstatic."
He added that those audience members unfamiliar with any of the four Harry Potter adventures "loved the story" and spoke of wanting to buy the book.
The movie stars Daniel Radcliffe as Harry Potter. Rupert Grint and Emma Watson play his best friends Ron and Hermione.
The story focuses on the young wizard's initiation into the world of magic as he begins his apprenticeship at Hogwarts School.
The film also boasts a glittering array of established stars, including John Cleese as ghost Nearly Headless Nick, Richard Harris as Headmaster Albus Dumbledore and Dame Maggie Smith as his deputy Minverva McGonagall.