Furness rose to fame in 1988, when she starred in the movie Shame, for which she won Best Actor awards from the Film Critics Circle of Australia and Golden Space Needle. Other roles included an episode of Halifax f.p. and The Flying Doctors. In 1993, Furness appeared as Chrissy in the television mini-series Stark starring Ben Elton and Jacqueline McKenzie. In 1995 she featured in the film Angel Baby directed by Michael Rymer and starring Jacqueline McKenzie and John Lynch. The film followed the story of two schizophrenics who met during therapy and fell passionately in love.