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In one scene, she is showering in a tent when the canvas is ripped away, exposing her to the rowdy applauding co-workers who have lined up their chairs to watch. “The first take, Sally hit the ground so fast that we couldn’t tell what she was doing,” said the director. For the second one, he and the actor Gary Burghoff stood “on either side of the camera with our pants down, so when the tent went up she saw the two of us standing there naked. That’s why she froze before falling, and how we got the shot we wanted.”

In Kellerman’s recollection, there was a third take with yet another naked colleague off-camera. “[Altman] had Tamara Horrocks, she was the more amply endowed nurse, without her shirt on,” she said. “So I attribute my Academy Award nomination to the people who made my mouth hang open when I hit the deck.”

Provided by The Guardian Sally Kellerman in Welcome to LA, 1976. Photograph: Everett Collection /Alamy

Kellerman conceded that “there was a lot of chauvinism” in the picture, though she believed that the humiliation served an important function for her character. “She grew up after that,” she said. “She’d been so uptight, so rigid, no sense of humour – and after all that went down, she started having a really good time, a real life.” She also considered the film a personal turning point. “For the first time in my life I took chances.”

In the director’s next film, the oddball comedy Brewster McCloud (also 1970), Kellerman played the mysterious Louise, who may be an angel or a reincarnated bird. Though she turned down a part in Altman’s Nashville (1975), she worked with him again on Alan Rudolph’s Welcome to LA (1976), which he produced, and is one of the many actors seen as themselves in his Hollywood satire The Player (1992). She appeared as a magazine editor, reportedly modelled on Liz Tilberis of Harper’s Bazaar, in Altman’s fashion-industry comedy Prêt-à-Porter (1994), and starred in an episode of the series Gun (1997), which he directed.

Kellerman was born in Long Beach, California, to John Helm Kellerman, an oil executive, and Edith, a piano teacher. She was educated at Hollywood high school, where her talent for singing and acting first emerged. At 18, she was offered a contract as a singer with the jazz label Verve Records. She later claimed that stage fright put paid to her hopes of performing, but also that she declined the contract in favour of pursuing her acting career, having recently begun taking classes alongside Jack Nicholson.

It was not until 1972 that she recorded her first album, Roll with the Feelin’. Her second, Sally, was released in 2009.

While working as a waitress, she began to get small parts in film, television and theatre. She had one line of dialogue in Reform School Girl (1957), her screen debut, as well as in the horror movie Hands of a Stranger (1962). She appeared in television series including The Outer Limits, in which a part was specially written for her by Joseph Stefano, the screenwriter of Psycho (1960), who had seen her in a play. She wore silver contact lenses as a psychiatrist who develops godlike powers in a 1966 episode of Star Trek. In The Boston Strangler (1968), she narrowly escapes being murdered by the title character, played by Tony Curtis.

She was in the 1966 stage version of Breakfast at Tiffany’s, starring Mary Tyler Moore and Richard Chamberlain. Beset by behind-the-scenes problems, the show closed after just four previews, having never officially opened. She also starred in the musical remake of Frank Capra’s 1937 melodrama Lost Horizon (1973), another notorious flop; its writer, the future activist Larry Kramer, described it as “the one thing I have done in my life that I truly regret.”

She turned down most film offers after M*A*S*H to concentrate on touring as a musician. Exceptions included the Neil Simon adaptation Last of the Red Hot Lovers (1972) and the crime caper Slither (1973). At the end of that decade she twice played the troubled mother of a teenage girl – first with Diane Lane in A Little Romance (1979) and then Jodie Foster in Foxes (1980).

Part of her skill was to bring charm and effervescence where previously there had been none, never more so than in her turn as a literature professor in Back to School (1986), a vehicle for the coarse, gravel-voiced comic Rodney Dangerfield. “The director said he felt that I helped make Rodney human, believable in a relationship,” she said. “Because I just had to love him and be sincere about it.”

Other film work included Blake Edwards’s comedy-drama That’s Life (also 1986), with Jack Lemmon and Julie Andrews, and Henry Jaglom’s mockumentary Someone to Love (1987), which featured Orson Welles’s final film appearance. Between 2013 and 2016, she played the mother of the comic Marc Maron in his fictionalised TV series Maron.

Kellerman was honest about having failed to capitalise on the success of M*A*S*H. “I began to believe my own publicity,” she said. “I’d been this overweight, not very confident girl, and now everybody was telling me I was the greatest … But instead I thought, ‘OK great, I guess I’ve got this acting thing down now. Time to work on my music’ … When it comes to building a career, I have never been the sharpest tool in the shed.”

In 2013, she published her memoir, Read My Lips: Stories of a Hollywood Life.

She is survived by Jack, her son from her second marriage, to the producer and manager Jonathan Krane, and by a daughter, Claire. Both Krane and Jack’s twin sister, Hannah, died in unrelated incidents three months apart in 2016. Her first marriage, to Rick Edelstein, ended in divorce in 1972.

• Sally Clare Kellerman, actor and singer, born 2 June 1937; died 24 February 2022