Brennan received excellent reviews as brothel madam "Billie" in George Roy Hill's Oscar-winning 1973 film The Sting as the confidante of con man Henry Gondorf (Paul Newman). Although her name was not often recognized by the general public, she became a favorite of many directors, in particular Peter Bogdanovich. She appeared in Bogdanovich's 1971 classic The Last Picture Show (for which she received a BAFTA nomination for best supporting actress) and his 1974 adaptation of the Henry James novella Daisy Miller. Bogdanovich was the only director who made use of her musical talents (before, she sang in performances off Broadway) when he cast her as Cybill Shepherd's crude, fun-loving maid in his 1975 musical flop At Long Last Love (which also starred Madeline Kahn; both Brennan and Kahn would work together in two more films: The Cheap Detective and Clue).
The actress also clicked with director Robert Moore and writer Neil Simon, appearing in Murder by Death (1976) and The Cheap Detective (1978). Both of these movies also starred James Coco and Peter Falk.
In 1980, Brennan received a best supporting actress Oscar nomination for her role as Goldie Hawn's nasty commanding officer in Private Benjamin. She reprised the role in the television adaptation (1981-1983), for which she won an Emmy (supporting actress) as well as a Golden Globe (lead actress). She has one additional Golden Globe nomination and six Emmy nominations.
After having dinner together one night in 1982, Brennan and Hawn left a restaurant. Brennan was hit by a passing car and was critically injured. She took three years off work to recover, and had to overcome a subsequent addiction to painkillers.
It was during this time that her performance as Mrs. Peacock in Clue (1985) reached theaters.
In recent years, Brennan has guest-starred in television, including recurring roles as the nosy Mrs. Bink in 7th Heaven and as gruff acting coach Zandra on Will & Grace. Eileen also did a memorable turn as Elliot's alcoholic-recovering mother on Thirtysomething.