"The whole thing looks beautiful," said the Telegraph's Anita Singh of a show she describes as "perfect entertainment for a Sunday night in autumn".
Carol Midgley of The Times praised the "standout" acting performances.
She said the series was "that rare creature: something that can entertain adults and children simultaneously".
Metro's Keith Watson was effusive too, despite being confused by its story.
"As the many characters tumbled off the page and on to the screen... the initial impression was one of bafflement," he concedes.
Yet his four-star review goes on to call the programme "a true feast for the eyes" with "fully formed and convincing" performances.
Set in an alternative reality full of airships, witches and giant polar bears, the eight-part drama is based on Northern Lights, the first book in Pullman's trilogy.
In the version of Britain depicted in the series, every character is accompanied by a daemon - a physical manifestation of their soul that takes the form of an animal.
The first episode of the series drew an average audience of 7.2 million viewers, according to overnight figures from Barb.
Its lead character is Lyra, a young girl who embarks on a quest to discover why children her age are being mysteriously abducted.
The Guardian's Lucy Mangan said 14-year-old Dafne Keen gives "a fierce, intelligent performance" as Lyra, while the Mail's Christopher Stevens said she and her fellow actors are "terrific".
Further series based on The Subtle Knife and The Amber Spyglass, the second and third books in the trilogy, have already been commissioned.
According to Mangan, the debut episode "gave every sign" the drama would have the "time and space to do them justice".
Published between 1995 and 2000, Pullman's books have previously been adapted for radio, film and the stage.
The film version, 2007's The Golden Compass, was not a box office success, though it did win an Oscar and a Bafta for its visual effects.
The TV version, a co-production with US network HBO, was largely shot in Wales with a large cast that includes James McAvoy and Ruth Wilson.
The BBC has not confirmed how much the show cost to make, though its budget has been reported to be between £40 million and £50 million.