Russell attended the American Academy of Dramatic Arts and made her Broadway debut in 1930 in the Theatre Guild's Garrick Gaieties. Four years later she was under contract to Metro-Goldwyn-Mayer (MGM) and made her film debut in Evelyn Prentice (1934). Throughout the 1930s she was regularly lent to other studios, and, when she did work for MGM, it was in roles rejected by Joan Crawford (Crawford, Joan) or Myrna Loy. Her best-known and most important performance came in His Girl Friday (1940), Howard Hawks's treatment of the play The Front Page. Playing opposite Cary Grant, Russell displayed expert comic timing as star reporter Hildy Johnson. The role was so successful that for the next decade she was often cast as the sharp-tongued, independent, and stylish career woman.

By the 1950s Russell had outgrown the career-woman roles and returned to the Broadway stage, winning a Tony Award in 1953 for her performance in Wonderful Town. One of her most memorable performances was in the title role of the long-running stage hit Auntie Mame (1956) and the subsequent movie version (1958), in which she played an unconventional woman whose nephew comes to live with her after his father's death. In the 1950s and '60s she enjoyed a broader range of roles in movies, giving notable performances in Picnic (1956), Gypsy (1962), and The Trouble with Angels (1966).