Morton became known to an international film audience in 1997, when she won wide acclaim for her wrenching, fearless portrayal of a young woman driven to promiscuous behavior by the death of her mother in Carine Adler's Under the Skin. The following year, she did starring work in The Last Yellow and Dreaming of Joseph Lees, playing the girlfriend of a small-time crook in the former and a dissatisfied young woman harboring romantic feelings for her long-absent second cousin (Rupert Graves) in the latter.

In 1999, Morton's name became an increasingly familiar one to American filmgoers, thanks to starring roles in two very different films. The first, Jesus' Son, cast the actress as a heroin addict, while the second, Woody Allen's Sweet and Lowdown, featured her as a shy, mute woman who gets used and abused by a legendary jazz guitarist (Sean Penn) whose musical talent runs in inverse proportion to his qualities as a human being. Heralded for both films, Morton scored a surprise Best Supporting Actress Oscar nomination for the latter. Not resting on the laurel, the actress immediately set to work with a pair of venerable cineastes, directors Julien Temple (in Pandemonium) and Amos Gitai (in his first English-language production, Eden).

Director Steven Spielberg soon followed Allen's lead, casting Morton in a small but pivotal role as a shivering, near-mute, clairvoyant "Precog" in his Blade Runner-esque mystery Minority Report, which premiered in the summer of 2002. Though the film would introduce Morton to her largest audience yet, it was a pair of independent features released in late 2002 and 2003 that would garner her even more significant critical attention. Teaming with the maverick Scottish director Lynne Ramsay, the actress would essay the enigmatic, directionless title character in Morvern Callar, a dreamy, elliptical adaptation of Alan Warner's cult novel. About a year later, Morton would see the release of In America, Jim Sheridan's acclaimed slice-of-life tale of an Irish family immigrating to New York City's Hell's Kitchen, for which she would receive her second Academy Award nomination, this time for Best Actress.