Brown pursued secondary education at the National Theatre School of Canada. She gained notice as a participating actor at the Stratford Shakespeare Festival, and spent several years honing her work on the stage.

Brown was born in Washington, D.C., the daughter of Elizabeth Ann (née Blair), a teacher, and Milton Henry Brown, a U.S. intelligence agent. Brown had a relationship with actor Richard Jordan. The two met during the filming of the miniseries Captain and the Kings in 1976. The couple lived together from 1976 to 1985, and they had one son, Robert, born in 1983.

Brown's first feature film 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, 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 for which she received her first Golden Globe Award nomination, in the category of Best Motion Picture Actress in a Comedy/Musical.

Other film roles include: The Astronaut's Wife (1999), Clint Eastwood's Space Cowboys (2000), Lars von Trier's Dogville, the Kevin Bacon-directed Loverboy (2005) and The Sentinel (2006).

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.

Brown is perhaps best known for her five-year run (1987-1991) on the Emmy Award-nominated comedy-drama series The Days and Nights of Molly Dodd. Brown played the title role, and she, and the show, earned a small but dedicated following. Brown received five consecutive Emmy Award nominations for each season, in the category of Outstanding Lead Actress in a Comedy Series, but never won. The show spent two years on NBC, then moved to the Lifetime cable channel for the remainder of its run.

Brown also appeared in other prime-time series including The Rockford Files, Kojak, Frasier, Smallville, Touched by an Angel, ER, and Ed.

Beginning in 2008, Brown has a recurring role, as Nina Sharp, in the television series Fringe, which premiered on September 9, 2008 on Fox.

Brown has been involved with theater since the beginning of her career. Among her earlier roles was a run as Lucy Brown in the 1976 production of Brecht & Weill's 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 the Broadway came in 1989, in the play Secret Rapture, written by David Hare.

Once "Molly Dodd" concluded, Brown became a prolific Broadway actress, appearing in a number of roles. Among them were roles in Tom Stoppard's Arcadia at Lincoln Center, two separate runs as Frau Schneider in the revival of Cabaret, and The Comedy of Errors for the New York Shakespeare Festival. She won a Tony Award in the category of Best Featured Actress in a Play, in 2000, for her role in the play Copenhagen. She played the role of the wife of physicist Niels Bohr. Brown played the lead role in The Clean House, by playwright Sarah Ruhl in 2006 at Lincoln Center.[citation needed]