Connell began her career with her husband Gordon, entertaining in San Francisco night clubs such as "The Purple Onion" and "The Hungry I". Eventually the couple moved to New York City, where Connell made her Off-Broadway debut in the 1955 revival of "The Threepenny Opera", a long-running hit at the Theatre de Lys. In the London production of "Once Upon a Mattress", Connell starred as Winifred, the role that Carol Burnett had originated in New York. Her Broadway debut came in the role of Mrs. Peachum in "Threepenny Opera" (1955).