Cavanagh made her film debut in Penny Marshall's A League of Their Own starring Tom Hanks, Geena Davis, and Lori Petty. Film critic Vincent Canby of the New York Times praised the film writing "A League of Their Own is one of the year's most cheerful, most relaxed, most easily enjoyable comedies. It's a serious film that's lighter than air, a very funny movie that manages to score a few points for feminism in passing." He went on to list Cavanagh as among "the excellent supporting players", as did film critic Jonathan Rosenbaum of the Chicago Reader.
