Her manager Kim Vasilakis confirmed the death on Tuesday saying the cause was bladder cancer.
Ms. Brennan had had a solid career on the New York stage and in films like The Last Picture Show and The Sting when she was cast for the film Private Benjamin a 1980 box office hit starring Goldie Hawn in the title role.
Ms. Brennan played Capt. Doreen Lewis the slow burning commanding officer of a pampered privileged young woman who joins the Army and finds that she isn t anybody s little princess anymore. The performance brought Ms. Brennan an Academy Award nomination for best supporting actress. She reprised the role in 1981 in a CBS sitcom based on the film with Lorna Patterson in the Goldie Hawn role. The TV performance brought Ms. Brennan the Emmy Award for best supporting actress in a comedy variety or music series.
But she was forced to leave Private Benjamin when she was hit by a car and critically injured in Venice Calif. Without her the series died in 1983.
While recovering Ms. Brennan became addicted to pain medication and underwent treatment. She later developed breast cancer.
She returned to television in 1985 in a new sitcom Off the Rack with Edward Asner but the show lasted only six episodes. Afterward she made guest appearances on other shows but she never recaptured the attention she had known in the past as the toast of Off Broadway in Little Mary Sunshine as a film actress in the 1970s and as an honored comedy star just before her accident.
Verla Eileen Regina Brennen was born on Sept. 3 1932 and grew up in Los Angeles the daughter of a newspaper reporter who also worked in sales and a former actress. Later in life dealing with her own alcohol dependency she talked about the alcoholism in her family when she was a child.
After attending Georgetown University she studied acting at the American Academy of Dramatic Arts in New York performed in summer stock and worked as a singing waitress.
Her first big role was as the title character in Rick Besoyan s Little Mary Sunshine a 1959 parody of operettas that played at the Orpheum Theater. She won an Obie Award for her portrayal of the show s spunky fluttery eyed heroine. A year later she complained to The New York Times that she had been hopelessly typecast as that kookie girl.
Perhaps to prove otherwise she promptly starred in the national tour of The Miracle Worker as Helen Keller s gravely serious teacher Annie Sullivan.
In 1963 Ms. Brennan earned positive reviews as Anna in a City Center revival of The King and I. In 1964 she was cast as Irene Molloy the young widow in the original Broadway production of Hello Dolly with Carol Channing.
Among later stage performances she appeared in John Ford Noonan s A Coupla White Chicks Sitting Around Talking a critically praised 1980 two woman show with Susan Sarandon and Martin McDonagh s dark comedy The Cripple of Inishmaan (1998) in which she played an alcoholic Irishwoman.
Ms. Brennan made her television debut in The Star Wagon a 1966 PBS special based on Maxwell Anderson s play about a man who invented a time machine. Her film debut came a year later in Divorce American Style a comedy starring Debbie Reynolds and Dick Van Dyke.
After a brief stint as an original cast member (along with Ms. Hawn) of Rowan and Martin s Laugh In the 1960s sketch comedy series she did her first picture playing a world weary Texas waitress in The Last Picture Show (1971) directed by Peter Bogdanovich.
Mr. Bogdanovich cast her again in Daisy Miller (1974) as a society hostess and in At Long Last Love (1975) as a singing maid.
Ms. Brennan played a madam with a heart of gold in the Oscar winning 1973 film The Sting and appeared in two comedy noir films written by Neil Simon Murder by Death (1976) and The Cheap Detective (1978).
In later years she appeared in Miss Congeniality 2 Armed and Fabulous (2005) as William Shatner s mother (despite being a year younger than he was). But she was most visible making guest appearances on television.
In addition to the Emmy she won Ms. Brennan received six other Emmy nominations. Two were for Private Benjamin. The others were for her work in Taxi Newhart Thirtysomething and Will Grace in which she played Sean Hayes s formidable acting teacher.
Throughout her career she talked openly about addiction. It s so horrible and it can be so disastrous yet there s something about the sensitivity of the human being that has to face it she said in a 1996 interview. We re very sensitive people with a lot of introspection and you get saved or you don t get saved.
Ms. Brennan was married from 1968 to 1974 to David John Lampson an aspiring actor. Their two sons Patrick and Sam survive her along with a sister Kathleen Howard and two grandchildren.