The Mad Men star - the daughter of famed playwright David Mamet - tried out for the secondary character of Shoshanna in 2010, but she was so ill at the table read, she was convinced show creator and star Lena Dunham and her casting directors would cut her from the shortlist.
Mamet admits she remembers very little about the script read itself because she had been downing cough medicine and sleep aid NyQuil the night before the audition.
Recalling that fateful day, she tells The New York Times Magazine, ""I called my agent and said, 'I think I may have lost this job. I'm so sorry.'""
However, Mamet's performance had come off much better than she could ever have imagined - and Dunham and co-producer Judd Apatow were such big fans of her work, they decided to expand the role of Shoshanna - a virginal, quirky girl obsessed with Sarah Jessica Parker's show Sex and the City - and make her one of the series' four main characters.
Dunham says, ""She definitely shifted my original conception of the character, which was a much more tangential girl, whose main job was to illuminate how un-Sex and the City this world was. But Zosia's read... gave me the sense that Shoshanna could be something much larger.""
Girls, which airs on America's HBO cable network, follows four 20-something girls as they try and make it in New York.