After making her Broadway debut as Rita in Craig Lucas' Prelude to a Kiss in 1990 (for which she received a Tony Award nomination), Parker came to prominence for film roles in Grand Canyon (1991), Fried Green Tomatoes (1991), The Client (1994), Bullets Over Broadway (1994), A Place for Annie (1994), Boys on the Side (1995), The Portrait of a Lady (1996), and The Maker (1997).

Among stage and independent film appearances thereafter, Parker received the 2001 Tony Award for Best Actress in a Play for her portrayal of Catherine Llewellyn in David Auburn's Proof, among other accolades.

She received both a Golden Globe and a Primetime Emmy Award for her portrayal of Harper Pitt in the acclaimed HBO television miniseries Angels in America in 2003.

In 2022, she reprised the role of Li'l Bit, which she had originated off-Broadway in 1997, in How I Learned to Drive on Broadway, a performance which earned Parker her fifth Tony nomination.

[3][4][5] Because of her father's career, Parker spent parts of her childhood in South Carolina, Tennessee, and Texas, as well as in Thailand, Germany, and France.

Parker starred with Kevin Kline in Grand Canyon (1991); with Kathy Bates, Mary Stuart Masterson, and Jessica Tandy in Fried Green Tomatoes (1991); with Susan Sarandon and Tommy Lee Jones in The Client (1994); with John Cusack in Bullets Over Broadway (1994); and with Drew Barrymore and Whoopi Goldberg in Boys on the Side (1995), as a woman with AIDS.

Parker's next role was in a movie adaptation of another Craig Lucas play, Reckless (1995), alongside Mia Farrow, followed by Jane Campion's The Portrait of a Lady (1996), which also starred Nicole Kidman, Viggo Mortensen, Christian Bale, John Malkovich and Barbara Hershey.

Parker's theater career continued when she appeared off-Broadway in Paula Vogel's 1997 critical smash How I Learned to Drive, with David Morse.

On December 7, 2003, HBO aired a six-and-a-half-hour adaptation of Tony Kushner's acclaimed Broadway play Angels in America, directed by Mike Nichols.

and a television film called Miracle Run, based on the true story of a mother of two sons with autism, as well as appearing in the lead role in Craig Lucas' Reckless on Broadway.

In 2006, Parker received the Golden Globe Award for Best Actress – Television Series Musical or Comedy, given by the Hollywood Foreign Press Association, for her lead role in Weeds.

She then portrayed Zerelda Mimms in the Andrew Dominik film The Assassination of Jesse James by the Coward Robert Ford, which opened in cinemas in September 2007.

Parker appeared in 2008's The Spiderwick Chronicles and in off-Broadway's Playwrights Horizons production in the New York premiere of Dead Man's Cell Phone, a new play by Sarah Ruhl, alongside Drama Desk Award winner Kathleen Chalfant.

Parker took the lead role in the Roundabout Theatre Broadway revival of the play Hedda Gabler, running from January through March 29, 2009.

[19] The play transferred to Broadway at the Samuel J. Friedman Theatre, with previews starting on September 20, 2016, officially opening on October 13, with Parker and Denis Arndt reprising their roles.

[20][21] She starred on Broadway in the Adam Rapp play The Sound Inside at Studio 54 starting on September 14, 2019, in previews, officially on October 17.

"[38] She also participates in a charity dinner for veteran victims of post-traumatic stress disorder organized by the David Lynch Foundation with Tom Hanks.