Parker maintained a strong theater presence in the early 1990s, but also built her reputation on the big screen, starring with Kevin Kline in Grand Canyon (1991), 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.
In the late 1980s, Parker moved to New York, where she got a job measuring feet at ECCO.
She dedicated the award to the late John Spencer, known for his work as Leo Mc Garry on The West Wing.
After receiving the award, Parker stated: "I'm really in favor of legalizing marijuana.
I don't think it's that controversial." In March 2007, Parker played the lead role in the television film The Robber Bride.
Her next role, Zerelda Mimms, in the Andrew Dominik film The Assassination of Jesse James by the Coward Robert Ford, opened in cinemas in September 2007.