Parkins began her career as a backup singer and dancer in the nightclub acts of stars like comedian George Burns. She made her film debut in the 1961 low-budget crime caper 20,000 Eyes, and guest-starred in television series such as Leave It to Beaver, The Untouchables, Perry Mason and The Wide Country.

Parkins was the only female star in the series through its entire run (1964–1969). In 1966, she was nominated for an Emmy Award as Best Actress in a Lead Role in a Dramatic Series, but lost to Barbara Stanwyck for The Big Valley. Parkins said while losing the award was painful, she was glad to have lost it to Stanwyck instead of Anne Francis, who was also nominated and whose work Parkins thought was “unfeminine.”

After visiting London in 1968 to be a bridesmaid in the wedding of Valley of the Dolls co-star Sharon Tate and director Roman Polanski, Parkins moved to England, where she starred in several productions, including Puppet on a Chain, Shout at the Devil, and The Mephisto Waltz. Parkins said she moved to London because it was relaxed, simple and she loved its traditions.

In 1991, Parkins starred in Canadian mystery series Scene of the Crime. She appeared in two Susann-inspired projects, the biography Scandalous Me and a segment of the Lifetime series Intimate Portrait.

In 2006, Parkins participated with Ted Casablanca on the audio commentary for the DVD release of Valley of the Dolls.