Avery completed her training at the American Academy of Dramatic Arts in New York. She had previously made her Broadway debut in May 1937, with the role of Goldie in the musical Orchids Preferred. In 1940/1941 she appeared on Broadway in the successful comedy Charley's Aunt. She played alongside José Ferrer the role of Amy Spettigue, one of the young naive girls. From November 1943 to May 1944, she played the role of Dorothy Ross on Broadway in the musical playWinged Victory by Moss Hart, a production of the US Army Air Forces, in over 200 performances. One of her partners was actor Don Taylor, whom Avery later married. Avery made her film debut in 1951 with the role of the young girl Marjorie in the film comedy Queen for a Day. In 1952, she played the role of Tracy McAuliffe, the wife of the movie character Boake Tackman embodied by Charlton Heston, in the MGM film drama Ruby Gentry. In 1956, along with Gordon MacRae, Ernest Borgnine and Dan Dailey, she was part of the cast for the musical The Best Things in Life Are Free, a film biography of three composers. She embodied Margaret Henderson, the wife of the music teacher and composer Ray Henderson. Despite a few more film roles, Avery has worked primarily as a television actress since the 1950s. She has appeared in continuous series roles, episode roles and guest roles in a total of over 40 television series. From 1953 to 1955, she embodied Peggy McNutley's wife as Ray Milland's wife in the US sitcom Meet Mr. McNutley. From 1960 to 1962 she took on the role of Anne Shelby in soap operaThe Clear Horizon; in it she played the wife of a US astronaut stationed in Cape Canaveral Air Force Station, who was attracted to another man. She had appearances in the television series Richard Diamond, Private Detective, Perry Mason, The Rifleman, Rawhide, Peter Gunn, Have Gun Will Travel,Laramie, The Virginian, Dr. Kildare, Daniel Boone, All in The Family, Charlie's Angels and Baretta. In the late 1970s, Avery ended her career as an actress. She returned to the camera for some sporadic film and television roles in the 1990s, including the comedy film Made in America, the comedy series Coach, and the 1999 filmThe Secret Life of Girls. Avery had been working in and around Los Angeles as a real estate broker since the 1960s.
Avery married actor Don Taylor in 1944, in whom she had met in the Broadway production "Winged Victory"; they divorced in 1955. The marriage resulted in two daughters. Avery died on May 19, 2011 at the age of 88 in her home in Los Angeles of heart failure.