Duke was born in Toronto, Ontario. She went to high school with Catherine O'Hara at Burnhamthorpe Collegiate Institute in Etobicoke; they first met in home room class. In 1976 Duke joined O'Hara as part of the Toronto version of the stage comedy troupe The Second City, while also making several appearances in the troupe's television series, SCTV. Duke became a regular on SCTV from 1980–81. She joined the cast of Saturday Night Live in 1981 when O'Hara suddenly dropped out of that show.
Duke was an Actress and Writer on SNL from 1981 to 1984. Duke was hired in place of Catherine O'Hara, who was chosen as a cast member when Dick Ebersol was hired following the termination of Jean Doumanian and most of her cast members. O'Hara backed out after SNL Writer Michael O'Donoghue yelled at cast and crew members for ruining the show during its sixth season. Duke's most popular character was probably Wendy Whiner, a woman who, with her equally whiny husband (Joe Piscopo), annoyed everyone she met. She is also remembered for appearing with Mr. T as the equally bizarre "Mrs. T" in a faux commercial for the real-life product "Mr. and Mrs. T's Bloody Mary Mix".
Duke went on to appear in such films as Club Paradise (1986), Groundhog Day (1993), Stuart Saves His Family (1995) and Portrait of a Serial Monogamist (2015), along with many television guest appearances.
In 2016, Duke joined the cast of Schitt's Creek playing dress shop owner Wendy Kurtz. The sitcom reunites Duke with her old SCTV castmate Eugene Levy.