She had a recurring role on the Showtime comedy-drama series Weeds (2009–2012) and received critical acclaim for her voice work in Charlie Kaufman's Anomalisa (2015).

At the age of 14, she attended acting workshops, taught by Lee Strasberg, and the Stagedoor Manor Performing Arts Training Center in Loch Sheldrake, New York.

Several television films followed, including a portrayal of an anorexic teenager in The Best Little Girl in the World, for which Leigh dropped to 86 pounds (39 kg) under medical supervision.

She played a virginal princess kidnapped and raped by mercenaries in Flesh and Blood (1985), an innocent waitress pursued by the psychopathic title character in The Hitcher (1986) (both films pitting her alongside Rutger Hauer), a mentally-disturbed, child-like young woman on the threshold of sexual awakening in the Southern Gothic film Sister, Sister (1987), and a young woman on the verge of a nervous breakdown in Heart of Midnight (1989).

This pretty, sweet-looking blonde has played a number of shy and innocent-looking women who are curious about sex; once they learn, they display wicked imaginations."

"[20] Leigh was cast in her first mainstream Hollywood studio film, the firefighter drama Backdraft (1991), in which she played a more conventional role, the girlfriend of lead actor William Baldwin.

She found more success in the gritty crime drama Rush (1991), portraying an undercover cop who becomes a junkie and falls in love with her partner, played by Jason Patric.

Reviewing Rush, Roger Ebert noted, "Leigh of course is a veteran by now of grubby characters in sleazy films; she has become one of the best young actresses by accepting roles some of her contemporaries would not even consider... After her extraordinary work as a doomed prostitute in Last Exit to Brooklyn, here she is again, looking sweet and wholesome, and descending into a world of people who have forgotten their better natures.

[24] Leigh co-starred with Kathy Bates as a tormented, pill-popping woman hiding a history of childhood sexual abuse in the adaptation of Stephen King's novel Dolores Claiborne (1995).

Leigh achieved her greatest acclaim in the role of Sadie Flood, an angry, drug-addicted rock singer living in the shadow of her successful older sister (Mare Winningham), in Georgia (1995).

For the role, Leigh dropped to 90 pounds (41 kg) and sang all of her songs live, including a rambling 8+1⁄2-minute version of Van Morrison's "Take Me Back".

[4] In a change of pace from her "bad girl" roles, Leigh played the fast-talking reporter Amy Archer in the Coen Brothers' comic homage to 1950s comedy, The Hudsucker Proxy (1994).

In another change of pace, she starred in Agnieszka Holland's version of the Henry James novel Washington Square (1997), as a mousy 19th-century heiress courted by a gold digger.

[34] Leigh had a brief role as a gangster's doomed wife in Sam Mendes's Road to Perdition (2002) and co-starred as Meg Ryan's brutally murdered sister in Jane Campion's erotic thriller In the Cut (2003).

Mick LaSalle of the San Francisco Chronicle commented that "As the downtrodden, sexy, trusting, and quietly funny prostitute, Leigh is, of course, in her element".

[47] In 2017, Leigh was reunited with her Hateful Eight co-star Tim Roth when the pair played a husband-and-wife team of contract killers in six episodes of Showtime's revival of David Lynch and Mark Frost's Twin Peaks.

Leigh played psychiatrist Dr. Ventress in the 2018 science fiction film Annihilation, alongside Natalie Portman, directed by Alex Garland and based on the novel by Jeff VanDerMeer.

In 2022, Leigh was cast in a lead role as Lorraine Lyon in the fifth season of the FX black comedy crime drama anthology series Fargo.

[51] Leigh plays an aging actress who makes jokes about her lack of Academy Award nominations and is fearful of losing her bisexual husband (Cumming).

The film was shot in 19 days on digital video,[4] and costarred the pair's real-life Hollywood friends,[51] including Kevin Kline, Phoebe Cates, Gwyneth Paltrow, Jennifer Beals, John C. Reilly, Parker Posey, and Leigh's sister Mina Badie.

On February 14, 2024, Leigh signed an open letter written by pro-Israel organization Creative Community for Peace criticizing attempts to remove Israel from Eurovision 2024.

[58] In 1982, Leigh's father, Vic Morrow, was accidentally killed along with two child actors when a helicopter stunt went wrong during the filming of Twilight Zone: The Movie.

[6][60] Speaking about her roles in smaller, independent films, she said, "I'd much rather be in a movie that people have really strong feelings about than one that makes a hundred million dollars but you can't remember because it's just like all the others.