Hunt began working in the 1970s as a child actress. Her early roles included an appearance as Murray Slaughter's daughter on The Mary Tyler Moore Show, alongside Lindsay Wagner in an episode of The Bionic Woman, and a regular role in the television series The Swiss Family Robinson. She appeared as a marijuana-smoking classmate on an episode of The Facts of Life. She also appeared as a young woman who, while on PCP, jumps out of a second-story window in a 1982 after school special called Desperate Lives (a scene which she mocked during a Saturday Night Live monologue in 1994). In the mid-1980s, she had a recurring role on St. Elsewhere as Clancy Williams, girlfriend of Dr. Jack "Boomer" Morrison. She remains best known for one of her earliest roles as Jennie in Bill: On His Own, costarring Mickey Rooney.

In the 1990s, after the lead female role in the short-lived My Life and Times, Hunt became well-known to television audiences in Mad About You, winning Emmy Awards for her perf