In March 1965, when LIFE photographer Bill Eppridge spent time on assignment with Judy Garland’s enormously talented daughter, Liza Minnelli, Liza was just turning 19 and launching what would prove to be a monumental career of her own. She was about to debut on Broadway in Flora the Red Menace, in a role that would make her, at the time, the youngest woman to win a Tony Award for lead actress. Also on the show’s creative team was composer John Kander and lyricist Fred Ebb. They would team up on such Broadway classics as Cabaret—later made into a movie starring Minnelli in her Oscar-winning role as Sally Bowles—and Chicago.

Liza allowed Eppridge into her spirited Flora rehearsals, and even invited him to her 19th birthday party in New York City, but in the end LIFE published just one of Eppridge’s photos. Here LIFE.com presents a series of pictures most of which never ran in LIFE of a legend in the making.

Liza, of course, was no stranger to show business: her mom was Judy Garland, her dad was the director Vincente Minnelli. She had performed with her mother at the London Palladium and had done a little work Off-Broadway but Flora the Red Menace would be her highest profile role to date, the gig that would nudge her out of the shadow of her famous parents and into another spotlight entirely.

Of Minnelli’s opening-night performance in Flora, LIFE wrote: “She acted and danced with an awkward, captivating charm, threw out ‘What-am-I-doing-here?’ looks, sang in a voice that boomed and belted, quivered sweetly, and occasionally got out of control which only added to her likability. . . . She certainly did look like her mother several rainbows ago. When she sang, there were echoes of Judy, too the old catches and wavers and throbs that made a song sound as if it were going through a nervous breakdown. But soon Judy’s image faded and Liza’s came into focus.”

In the decades since Eppridge made these intimate shots of the budding star, Liza has performed at the world’s most famous concert halls, racked up countless awards for her singing and acting and delighted new generations of fans with scene-stealing appearances in contemporary pop-culture touchstones like Arrested Development. But her early years truly were something special. As Liza told LIFE in 1965: “Eighteen is great, but 19 is best of all. That’s when you’re opening in your first Broadway show.”

Surrounded by friends, and in the embrace of fiancé Peter Allen   she'd marry the Australian entertainer two years later   19-year-old Liza Minnelli cuts her birthday cake in 1965.

Surrounded by friends, and in the embrace of fiancé Peter Allen—she’d marry the Australian entertainer two years later—19-year-old Liza Minnelli cut her birthday cake in 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli studies sheet music in rehearsals for Flora the Red Menace in 1965, a new musical in which she'd play a bohemian fashion designer during the Great Depression.

Liza Minnelli studied sheet music in rehearsals for Flora the Red Menace in 1965, a new musical in which she’d play a bohemian fashion designer during the Great Depression.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli runs lines with her Flora the Red Menace costar Bob Dishy. In the show, Liza's Flora falls for his character, a fellow designer who pulls her toward Communism.

Liza Minnelli ran lines with her Flora the Red Menace costar Bob Dishy. In the show, Liza’s Flora falls for his character, a fellow designer who pulls her toward Communism.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli and Bob Dishy are put through their paces by Flora the Red Menace choreographer Lee Theodore.

Liza Minnelli and Bob Dishy were put through their paces by Flora the Red Menace choreographer Lee Theodore.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli, 1965.

Liza Minnelli, 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli, 1965.

Liza Minnelli, 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli, 1965.

Flora the Red Menace rehearsals, 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli huddles with Flora the Red Menace choreographer Lee Theodore (right) and an unidentified man (possibly Fred Ebb).

Liza Minnelli huddled with Flora the Red Menace choreographer Lee Theodore (right) and an unidentified man (possibly Fred Ebb).

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli burns up the floor at her 19th birthday party at Il Mio, a disco inside Delmonico's Hotel in New York, March 1965.

Liza Minnelli burned up the floor at her 19th birthday party at Il Mio, a disco inside Delmonico’s Hotel in New York, March 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli, 1965.

Liza Minnelli, 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli busts out the hottest dance of the day, "the Frug," at her birthday party in 1965.

Liza Minnelli busted out the hottest dance of the day, “the Frug,” at her birthday party in 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Shoes kicked off, head thrown back, 19-year-old Liza Minnelli belts out a song for birthday party guests in 1965. From LIFE's report: "When a friend scolded her for singing for free she said, 'I don't care, I sing for me.'"

Shoes kicked off, head thrown back, 19-year-old Liza Minnelli belted out a song for birthday party guests in 1965. From LIFE’s report: “When a friend scolded her for singing for free she said, ‘I don’t care, I sing for me.'”

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli reacts as an unidentified well-wisher at her 19th birthday party presents her with a swan-shaped balloon.

Liza Minnelli reacted as an unidentified well-wisher at her 19th birthday party presented her with a swan-shaped balloon. Seated beside her was Peter Allen.

Bill Eppridge The LIFE Picture Collection/Getty Images

Liza Minnelli, 1965.

Liza Minnelli, 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

Birthday girl Liza Minnelli gets down on the floor with her guests, March 1965.

Birthday girl Liza Minnelli got down on the floor with her guests, March 1965.

Bill Eppridge The LIFE Picture Collection/Getty Images

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