Born in New York City and raised on Long Island, she moved to Los Angeles when her father, Alec Alexander, an agent who handled at that point such notables as Frank Gorshin and Sal Mineo, decided to make the switch from the east to the west coast. A successful child actress, Alexander had appeared on TV and radio by the time she was a junior at UCLA. She made her feature movie debut, aged fourteen, in the John Cassavetes film Crime In The Streets.
Alexander first broke into the soap opera genre by playing Susan Hunter Martin on Days of our Lives from 1966 to 1973. A popular actress, much of the show's early success had to do with Susan's rivalry with Julie Olson (played by Susan Seaforth Hayes). In 1973, Susan H. Martin was written out of the show temporarily when the Days casting office hit a snag renewing her contract and the contract lapsed. ABC Daytime rushed to offer her a then-unheard of salary/perks package to join General Hospital. When Susan H. Martin finally returned to Days, a new actress played her. A few months later, she started on General Hospital, playing the role of Dr. Lesley Webber, which would become her most popular and longest-tenured. She stayed with the show for eleven years, leaving in 1984. In 1986, she was offered a big salary to portray absent McKinnon matriarch, Mary, on Another World. When the commute from her home in Los Angeles to Another World's studio in New York City proved to be difficult for her, she left in 1989. In 1996, she returned to the role of Lesley on General Hospital which she continued playing until 2009.
Her career began as a child actress in radio and television, and has spanned virtually all forms of stage and screen (large and small) dramatic and comic entertainment---including, as a teenager, playing the daughter of a lawyer and a former fashion buyer (Hume Cronyn and Jessica Tandy) on the short lived NBC radio comedy-drama, The Marriage (1953–1954).
She has produced for both network and cable television, spoken as guest lecturer/speaker to groups from charities, to civic groups to college audiences. In a 1981 People Weekly interview, she called the late Gloria Monty "a wonderfully bossy little lady".