She is best known for her role as Joanna "Joey" Drayton, the European-American ingénue who brings home an African-American fiancé to meet her parents, in the 1967 film Guess Who's Coming to Dinner. She was chosen for the role due to her striking resemblance to the actress playing her on-screen mother, Katharine Hepburn. This comparison was no coincidence, as she was Ms. Hepburn's real-life niece.
Houghton has had an extensive career onstage and in films. In 2004, she portrayed Mrs. Spaulding, one of the trustees of Indiana University, in the feature film Kinsey.