Duffy's early career included parts in soap operas like One Life to Live. Duffy also appeared in movies such as Night Warning (1981) and Cutter's Way (1981).

Duffy joined the cast of the television series Newhart in its second season, playing the role of Stephanie Vanderkellen, which is probably her most popular role. She earned Emmy Award nominations for Outstanding Supporting Actress in a Comedy Series in the role every year from 1984-1990. She also received a Golden Globe nomination and won three Viewers for Quality Television Awards for her work.

After the end of Newhart, Duffy joined Designing Women, essentially replacing Delta Burke who was let go after quarrels with producers. Duffy played the newly-created role of Alison Sugarbaker. Duffy's season was the show's highest rated, but producers chose not to have her return for what would be its final year.

Duffy now does occasional television guest spots and movies.