Jolie's film, distributed by Universal, pulled in roughly $46.05 million in its four-day domestic launch, falling short of Sunday's $47.3-million studio estimate.
The drama, which cost about $65 million to make, is based on Laura Hillenbrand's 2010 nonfiction bestseller about Louis Zamperini, an Olympic runner turned war hero. It rounded out the top three.
Though it has received mixed reviews from critics, audiences gave it an A- grade with audience polling firm CinemaScore. It has a 51% "fresh" rating on Rotten Tomatoes.
Fellow holiday box office newcomer, "Into the Woods," ended up ahead of the biopic with about $46.14 million. It came in second to "The Hobbit: The Battle of the Five Armies," which topped the box office for the second weekend in a row.
Directed by Rob Marshall, Disney's musical drama is a modern twist on several fairy tales and stars
Going into the weekend, tracking suggested both "Unbroken" and "Into the Woods" would make far less than their final debut figures. Jolie's "Unbroken" was expected to open to up to $25 million, while "Into the Woods" was poised to make up to $30 million.
Analysts predict 2014 will end up pulling in $10.4 billion to $10.5 billion at the box office.