The new live-action adaptation directed by Kenneth Branagh and starring Lily James and Richard Madden, earned $70.1 million over the weekend.
The success of Cinderella replicates that of previous Disney live-action films including Maleficent.
Liam Neeson saw his star falter with Run All Night making just $11 million.
The New York crime saga, co-starring Ed Harris, marked the weakest debut weekend for Taken star Liam Neeson as an action film lead.
Cinderella follows the box office lead of Into the Woods, based on the Stephen Sondheim musical, which made more than $173 million worldwide to date.
Live action Disney adaptations of The Jungle Book, Beauty and the Beast and Dumbo are all on the way.
A sequel to Tim Burton’s Alice in Wonderland is also due to be released in 2016.
This year will also see Disney releases The Avengers: Age of Ultron and Star Wars: The Force Awakens.
Elsewhere in the box office chart, last week’s top film, the South African sci-fi thriller Chappie from District 9 director Neill Blomkamp, dropped to fifth with $5.8 million.
Kingsman: The Secret Service and Focus rounded out the top five.
North American box office Top 5:
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