Owens moved to England in 1933 with her parents (her father Arthur Owens was later to become an MI5 double agent), and ten years later, at age 18, she made her motion-picture debut in Val Guest's musical comedy Miss London Ltd. The following year, she had a small role in Harold French's social satire English Without Tears. Her career continued in this manner for a few years, Owens getting ever-larger roles in movies.

Owens spent the rest of 1957 working mostly on loan-out, but it was a successful Fox production that secured her best known role—as Hélène Delambre, the wife of scientist André Delambre in The Fly (1958), co-starring with David Hedison and Vincent Price. Owens carried much of the film's narrative, which was largely told in flashback from her character's point of view.

Subsequent films never reached the same level of success as The Fly. She co-starred with Jeffrey Hunter and David Janssen in a 1960 war film, Hell to Eternity, then in 1961 appeared in the threadbare, backlot POW/jungle chase drama Seven Women from Hell. Owens made occasional television appearances, on series such as Perry Mason and Burke's Law, but these were relatively infrequent. Owens also starred in one of the 17 episodes of Alfred Hitchcock Presents directed by Hitchcock himself, "The Crystal Trench" (1959).

By 1965, she was working in Black Spurs, one of Producer A.C. Lyles' B-Westerns, renowned for their use of aging genre stars. Owens retired from movies after portraying Richard Egan's love interest in the low-budget espionage thriller The Destructors (1968). Her last professional appearance was in an episode of Lassie (1968).