Alexander was born in New York City and raised on Long Island. She moved to Los Angeles when her father, Alec Alexander, an agent who handled such notables as Frank Gorshin and Sal Mineo, decided to make the switch from the East to the West Coast. Alexander had appeared on TV and radio by the time she was a junior at UCLA. She made her feature movie debut at age 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. In 1973, the character of Susan was written out of the show temporarily during contract negotiations with Alexander. ABC Daytime rushed to offer her a then-unheard of salary/perks package to join General Hospital. When Susan finally returned to Days, a new actress, Bennye Gattleys played her.
Alexander's role on General Hospital, Dr. Lesley Williams (Faulkner Webber), would become a long-running role. She stayed with the show for eleven years as one of the show's most popular leading ladies, leaving in 1984 after a contract dispute. In 1986, she was offered a big salary to portray 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 the show, filming her last scene in 1989, but briefly returned for a guest appearance in 1991. In 1996, she returned to the role of Lesley (brought back from the dead after almost 13 years!) on General Hospital, which she continued playing on a recurring basis until 2009 when the character simply faded from view. She reprised the role in time for the show's 50th anniversary in 2013 and remains on canvas as a recurring character.