Trained for a career in singing, Dunne went to New York City hoping to join the Metropolitan Opera Company but was rejected. Instead she joined the Chicago touring company of the musical comedy Irene in 1920. Several Broadway stage roles followed, most notably that of Magnolia Hawks in a touring production of Show Boat (1929), which won her a contract with RKO film studios.

Dunne's first motion picture, Leathernecking (1930), was not memorable, but with the release of Cimarron in 1931, she became a popular success. After Cimarron, she appeared in some 40 feature-length films. These included both dramatic roles—as in Back Street (1932); Magnificent Obsession (1935), with Robert Taylor; Love Affair (1939), with Charles Boyer; Anna and the King of Siam (1946), with Rex Harrison; and I Remember Mama (1948)—and roles in a number of comedies—such as Roberta (1935), with Fred Astaire and Ginger Rogers; Show Boat (1936); and The Awful Truth (1937) and My Favorite Wife (1940), both with Cary Grant. She retired after making It Grows on Trees in 1952. Thereafter she occasionally appeared on television, but the remainder of her life was largely devoted to civic affairs.