In 1924 Williams moved to New York, where he was cast in a series of successful Broadway productions. He would appear in over 30 Broadway plays over the next four decades, performing on stage with performers such as Claudette Colbert in Clifford Grey's "A Kiss in the Taxi" in 1925, Helen Hayes in J. M. Barrie's "Alice Sit-by-the-Fire" and Gertrude Lawrence in George Bernard Shaw's "Pygmalion" in 1946. In 1953, Williams won a Tony Award for Actor, Supporting or Featured (Dramatic) for his role as Chief Inspector Hubbard in Frederick Knott's "Dial M for Murder" on Broadway. Soon afterwards, when Alfred Hitchcock adapted the play to a film version released in 1954, he cast Williams in the same role.