Brown was born in Washington, D.C., the daughter of Elizabeth Ann (née Blair), a teacher, and Milton Henry Brown, who worked at the Central Intelligence Agency. She graduated from The Madeira School in McLean, Virginia, and then pursued acting at the National Theatre School of Canada, graduating in 1969. She gained notice as a participating actor at the Stratford Shakespeare Festival and spent several years working on the stage.

Brown also appeared in other prime-time series including The Rockford Files, Kojak, Frasier, Smallville, Touched by an Angel, ER, and Ed. In 1975 she appeared in one episode of the television mini-series Wheels. Beginning in 2008, Brown starred as Nina Sharp in the Fox television series Fringe. Brown also appeared in several seasons of the Netflix comedy-drama series Orange is the New Black as fictional television personality Judy King, an inmate loosely based on Martha Stewart.

Brown has been involved with theater since the beginning of her career. She appeared in the 1975 New York Shakespeare Festival production of The Comedy of Errors. Among her earlier roles was a run as Lucy Brown in the 1976 production of The Threepenny Opera, produced by Joe Papp and directed by Richard Foreman. She left the production for film work, but after being away from the production for eight months, Ellen Greene, who was playing the part of Jenny, fell ill. Brown astounded the stage manager of the production by coming in and, with one hour of rehearsal, put on a “brilliant” performance as Jenny. Her first major appearance on Broadway came in 1989, in the play Secret Rapture, written by David Hare.

Brown had a relationship with the late actor Richard Jordan, whom she met while filming the miniseries Captains and the Kings in 1976. The couple lived together from 1976 to 1985; their son Robert Anson Jordan III was born in 1983. She dated playwright David Hare from 1985 to 1990; he referred to her as his muse. She mentioned on Johnny Carson in 1989 that she is a Democrat.

Brown’s first feature role was in the Oscar-winning 1973 film The Paper Chase; her first major starring role was in The Choirboys in 1977. Among her other film credits were Altered States (opposite William Hurt), One Trick Pony (with Paul Simon), the film Stealing Home (opposite Mark Harmon) and A Flash of Green (1984). Her arguably highest profile film role to date was the romantic lead opposite John Belushi in Continental Divide (1981) for which she received her first Golden Globe Award nomination, in the category of Best Motion Picture Actress in a Comedy/Musical.

Brown appeared in several television movies and miniseries, primarily during the 1980s. A high-profile role as Jacqueline Kennedy in the 1983 TV miniseries Kennedy earned her a second Golden Globe nomination, for Best Actress in a Mini-Series or Motion Picture Made for Television, as well as a BAFTA nomination. She also appeared in several other programs about the Kennedys, including the 1996 miniseries A Season in Purgatory, which was a thinly veiled portrait of the family, as well as an appearance as Anna Roosevelt in a telefilm about Franklin Delano Roosevelt and Eleanor Roosevelt.

Her voiceovers are heard on a number of documentaries, including PBS’s American Experience series and the 2007 PBS series The Mysterious Human Heart. Other documentary narrations include the scientific series The Secret Life of the Brain, a documentary on Aimee Semple McPherson, which aired in April 2007, and a 2006 PBS documentary about Marie Antoinette. In April, 2010, she co-narrated the PBS special The Buddha with Richard Gere.