Although Garland was initially supportive of her then 18-year-old daughter Liza's show when they sang together at the London Palladium in 1965, her pride turned to fury.
In an extract from Liza's new memoir, Kids, Wait Til You Hear This! shared by People magazine, the Cabaret star wrote: "After my first song [on opening night] I heard her shout, 'Yeah, baby! Go get 'em!'"
"After the second song, another 'Yeah!' but not quite as strong. By the third song, let's just say she was losing enthusiasm.
"I heard her whispering to our producer, Harold Davison, 'Harold, get her off my f***ing stage!'
"I just kept singing to wild applause as Mama fumed. I had a stunning realisation. I had begun the night as Mama's daughter. Now, I was onstage with Judy Garland."
Elsewhere in her memoir, Minnelli, 79, shared that Garland allowed the star and her half-siblings, Lorna, 73, and Joey Luft, 70, to decide whether or not to join her on tour.
Minnelli - whose father director Vincente Minnelli, was married to Garland from 1945 until 1951 - recalled: "I'll never forget the day she sat us down and gave Lorna and me a choice; Joey was less than one year old.
"We could stay in school in Los Angeles. Or we could come on the road with her. We'd be in and out of different hotels, schools (I'd eventually attend 22 of them), and cities. 'When do we leave?' we answered in unison."
As a teenager, Minnelli cared for her mother - who had Lorna and Joey with late producer Sidney Luft, whom she was married to from 1952 until 1965.
"At 13, I was my mother's caretaker - a nurse, doctor, pharmacologist, and psychiatrist rolled into one. I lost count of the times I called doctors to say she'd run out of pills. I'd say, 'I'm a kid! Please fill my mama's prescription!'"
Garland died from an accidental drug overdose in June 1969, and Minnelli believes her "final gift" from The Wizard of Oz legend was inheriting her battle against substance abuse.
"I cried for eight straight days," she wrote in her memoir.
"Stress and tension overwhelmed me. I was reeling, and a doctor prescribed Valium to help me relax just before the funeral. What began as a one-day blessing soon turned into a habit, then a full-blown case of addiction in the years ahead.
"It was a final gift, a genetic inheritance from Mama I could not escape."
Minnelli was "convinced" she did not have a problem when her sister encouraged her to go to rehab in 1984.
Less than a year later, Elizabeth Taylor - who was herself newly sober - urged Minnelli to go back to rehab and take her problem seriously.
Minnelli checked into rehab again in 2015 and takes her sobriety seriously these days.
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