Dennis' high-pitched, neurotic style lent itself to quirky, eccentric roles in films such as "Splendor in the Grass" (1961, her debut). Her memorable performance as the irritating yet vulnerable young faculty wife in "Who's Afraid of Virginia Woolf" (1967) earned her an Oscar for Best Supporting Actress, and her portrayal of an idealistic teacher in an inner-city school in "Up the Down Staircase" (1967) won her a Best Actress accolade from the Moscow Film Festival.
Dennis turned in some fine performances in later films, notably "Come Back to the Five and Dime, Jimmy Dean, Jimmy Dean" (1982) and, in a hilarious cameo, Bob Balaban's overlooked "Parents" (1989). She made her final onscreen cameo as the wife of Charles Bronson in Sean Penn's directorial debut, "The Indian Runner" (1991), before her death the following year from ovarian cancer at age 54.