The 'Holiday in the Wild' star knew he wanted to be an actor from a young age so was delighted when he realised the 'Cabaret' star was staying nearby and sought her out in her hotel room.
Speaking on 'The Kelly Clarkson Show', Rob said: "I'm 10 years old, wanting to be a child actor and I'm living in Dayton, Ohio. There is nothing happening, and it's the mid-1970s."
Rob admitted that the meeting came about after he spotted the legendary star's name on a luggage label.
He explained: "I go to the front desk and I ask, 'What room is Liza Minnelli in?' And they tell me!
"What were they thinking? I was a 10-year-old boy! I just flat out asked, and I went up and knocked on the door in the middle of the day.
"They (Liza and her then-husband Jack Haley Jr) were in robes and eating chocolate and drinking red wine. I said 'Hi, I'm Rob Lowe and I want to be an actor.' "
The 55-year-old hunk says that Liza left a lasting impression on him.
Rob said: "She was awesome. She invited me into the room. She was so nice to me, and Liza was fascinated and wanted to know why I wanted to be an actor. She was awesome!"
And to this day, the former 'West Wing' star counts the 73-year-old actress as a friend.
He added: "Now we are friends, she's the best."
Meanwhile, Rob recently claimed his movie 'Holiday in the Wild' had more views on Netflix than Martin Scorsese's 'The Irishman'.
Rob, who stars in the festive flick alongside Kristin Davis, said: "I just did a movie for Netflix, it was the number one movie that they have.
"It was a stupid Christmas elephant movie. Take that Martin Scorsese. They were like, 'Don't tell anybody.'"