NEW YORK — When Cristin Milioti arrived at her final audition for the musical ‘‘Once,’’ her palms were slick with sweat, and she felt like she was going to pass out.

These were no ordinary audition nerves, though. In fact, Milioti, then 24, was already the hands-on favorite of the director, John Tiffany, who had been blown away by her acting in an earlier meeting.

The problem was the piano. As ‘‘Once’’ fans know, the lead female, Girl, is a Czech immigrant in Dublin who plays the piano beautifully and writes songs. But Milioti’s piano playing was minimal — she didn’t know how to read music, and the music director, she says, had deemed her ‘‘unteachable.’’

So the creative team had given her 10 days. Ten days to learn two key songs in the show — one classical, one contemporary. Those 10 days had been miserable. She had practiced seven, eight, even 10 hours a day, borrowing piano time at theaters around the city and a keyboard for nighttime. Since she couldn’t read notes, her friend had made a chart of the songs: numbers for fingers, letters for notes.

And here she was, back in the audition room. ‘‘I messed up the Mendelssohn,’’ she says. ‘‘But ‘The Hill,’ I nailed. I knew that. I left and called my boyfriend. I told him, well, I’ve done the best I could.’’

‘I messed up the Mendelssohn. But “The Hill,” I nailed. . . . I told [my boy­-friend], well, I’ve done the best I could.’

Anyone who has seen ‘‘Once’’ knows the rest of the story. Milioti got the job, and luminous reviews as Girl. And she was nominated for a Tony as best actress in a musical, alongside such Broadway greats as Audra McDonald in ‘‘The Gershwins’ Porgy and Bess’’ and Jan Maxwell in ‘‘Follies.’’

‘‘I can’t believe I am even performing on the same street as these women, not to mention having my name called out along with theirs,’’ says Milioti, now 26, slight and winsome, as she wolfs down a tuna sandwich in her publicist’s office after a recent matinee performance.

So convincing is Milioti’s Czech accent onstage that one imagines she’ll at least sound vaguely European in person. But she’s a Jersey girl — from Cherry Hill, N.J., to be exact, where she attended public high school. (It was at high school, amazingly, that she appeared in her last musical.)

After high school, Milioti spent a year studying at New York University’s Tisch School of the Arts — an unhappy year, she says. ‘‘I wasn’t a very good student,’’ she says. ‘‘I prefer to learn by experience.’’

Luckily, she was quick to get roles, and soon she had racked up a couple of Broadway credits — ‘‘The Lieutenant of Inishmore’’ and ‘‘Coram Boy’’ — as well as a number of off-Broadway roles. But no musicals. ‘‘I’ve tried out for lots of them, but it was never right,’’ Milioti says, allowing that she even had a session with Julie Taymor to explore playing Mary Jane, the girlfriend in ‘‘Spider-Man: Turn Off the Dark.’’

‘‘Some actors just have a quality, a way of combining music and character and story, where everything just falls into place,’’ says Tiffany, the Tony-nominated director of “Once.” ‘‘She is one of those actors who is all too rare in that way.’’

The day before he met Milioti, at a New York workshop reading of ‘‘Once’’ in early 2010, a friend had warned him that the actress, who was only reading a supporting role, would ‘‘blow his mind.’’ He was skeptical. Then he met her.

‘‘Within three seconds, I was obsessed,’’ he says. After the reading, he sent word to her agent that he wanted to see her for the role of Girl (he was casting for the show when it was developed at the American Repertory Theater in Cambridge).

‘‘Do you play the piano?’’ the agent asked Milioti. ‘‘Well, I could go in and fake it,’’ she replied.

At first she did — she knew a Regina Spektor song by heart. But soon enough the musical director, Martin Lowe, was asking: ‘‘What do you mean, you can’t read it?’’ Tiffany, though, was dead set on the actress, and thus followed the 10-day piano immersion.

‘‘She came in and wow, she nailed it,’’ says Tiffany, sounding like a proud papa. Milioti got the call a half-hour later, on her way into another audition. ‘‘I was floating,’’ she says.

After Cambridge came the off-Broadway production, at the New York Theatre Workshop, and then of course the move to Broadway. Milioti knew at any time she could be replaced for a bigger name, but she wasn’t. ‘‘I couldn’t control those things, but I told myself that whatever happened, I’d had a life-changing experience, working on this show with these people, everyone so passionate about it. I’ve never had that,’’ she says.