Duffy was born in Minneapolis, Minnesota, in 1951, the daughter of Joseph Hinds and Mary Duffy. Her early career included parts in soap operas such as One Life to Live, The Doctors, and Love of Life. Duffy also appeared in movies such as Night Warning (1981) and Cutter's Way (1981). She made an appearance on the television sitcom Cheers during the show's first season in 1982; she had been considered for the role of Diane Chambers, the sitcom's female lead.

Duffy graduated from the American Academy of Dramatic Arts in New York in 1972. She has been married since 1984 to actor Jerry Lacy, co-star of Dark Shadows and Love of Life, and has two children, Kerry Kathleen and Daniel. They live in Los Angeles.

After being an unfamiliar Actress in prime-time, Duffy joined the main cast of the sitcom Newhart during its second season in 1983 as the Stratford Inn's self-infatuated upper-class maid. She had initially made an appearance in the 14th episode of the first season of the series, playing the part of then-maid Leslie Vanderkellen's cousin. It is perhaps her most popular role and one she played for seven seasons. She earned Emmy Award nominations for Outstanding Supporting Actress in a Comedy Series for the role every year from 1984 through 1990. She also received a Golden Globe nomination and won three Viewers For Quality Television awards and 5 American Comedy Awards nominations for her work. Julia was actually pregnant during several episodes of Newhart. To hide it, she wore baggy clothes and stood behind furniture. She remains close to Newhart.

After the end of Newhart in 1990, Duffy briefly starred in the sitcom Baby Talk alongside George Clooney but asked to be released after Clooney walked off the troubled set. The new producers accommodated her, allowing her to then join the cast of Designing Women. Baby Talk was then retooled and Duffy was replaced by Mary Page Keller. She worked again with Clooney some years later in the Coen Brothers' comedy Intolerable Cruelty. In 1991, she joined the cast of Designing Women, essentially replacing Delta Burke, the show's breakout star, who was fired after quarrels with producers. Duffy played Allison Sugarbaker, Burke and Dixie Carter's previously unseen cousin on the show. Duffy's tenure on the sitcom's sixth season turned out to be the highest-rated season in the show's history, partly because of the highly publicized cast additions of Duffy and Jan Hooks. However, because of conflicting ideas about her character she was amicably released from her contract thus leading her to be replaced by Judith Ivey.

From 1993 to 1995, Duffy played Barb Ballantine on the short-lived comedy series The Mommies. Duffy played Lindsay Mercer, one of the failed buyers of Winfred-Lauder and the ex-wife of "Lord Mercer" on The Drew Carey Show. She has a recurring role on the Nickelodeon series Drake & Josh as Linda Hayfer, a high school English Teacher who despises Drake. She appeared on The Suite Life of Zack & Cody as the rich mother of Jason, a boy who goes on a date with Maddie Fitzpatrick (Ashley Tisdale).

On September 19, 2014, Duffy appeared on Ken Reid's TV Guidance Counselor Podcast.

In recent years she has been seen in recurring roles on HBO's Looking and Showtime's Shameless, as well as Scream Queens, Key and Peele, and other guest roles. She has been very active in the theatre, appearing in 5 plays in 7 years-'Little Foxes' and 'The Heiress' at the Pasadena Playhouse, 'boom' with Furious Theatre, 'Guess Who's Coming to Dinner' at the Huntington Theatre in Boston, for which she received an IRNE Award Nomination for best supporting Actress in a drama; and most recently in 'Sex and Education' at the Laguna Playhouse in April 2016. She will next appear on stage in 'Rancho Viejo' at Playwright's Horizons in fall of 2016. She has written a book, Bad Auditions, published by Smith and Kraus, which will be released in 2017.