Griffiths was a relative newcomer when cast in the film ''Muriel's Wedding (1994) as the loyal friend Rhonda, and the success of this film furthered the careers of both Griffiths and her costar Toni Collette.
She received an Academy Award nomination for Best Supporting Actress for her role in Hilary and Jackie (1998). Although a sought after actress in Hollywood productions, she returns to Australia frequently and continues to act in Australian films. Her American roles have required her to master an American accent, and in the 2001 film Very Annie Mary Griffiths adopted a Welsh accent to star with a predominantly Welsh cast as a young woman from the Valleys of South Wales.