During that show, Buscemi told the late-night host that Pink ran up to him before she was famous and said her stage name was inspired by his character, Mr. Pink, from his 1992 film Reservoir Dogs.
Asking Pink if the story, which he called "pretty insane" was true, the singer confirmed it was indeed "a real story."
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"But to be fair, I ran at him on a New York street. I physically — I'm like a hummingbird with my love," Pink said. "I'm very aggressive."
"I remember I was dressed in, like, a silver ensemble and I had short pink hair and a tongue ring and I [was like], 'You're Steve Buscemi and you're Mr. Pink and I'm Pink and you're pink and I'm going to be so famous and I just love you,'" she continued. "And he's like, 'What the f---?' He was like, 'Ahhh.' I would've reacted that way too. I was a lot."
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When asked by Fallon, 46, if the pair have met again since that day so many years ago, Pink said they have not.
"No. I mean, all this time, for like 20 years, I was like, 'That guy hates me,'" she joked.
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Back in early 2020 during Buscemi's Tonight Show appearance, the actor similarly recalled his initial meeting with Pink.
"I remember she did say her name was Pink," Buscemi recalled. "She said, 'I'm Pink and I have an album coming out soon.' This was like 20 years ago."
"And she said, 'I got my name sort of because of your character in Reservoir Dogs," he continued. "And it was very flattering — this was Pink ... but I didn't know who she was."
Explaining that he was "so anxious and nervous" at the moment because he was set to meet Paul McCartney later on, Buscemi added, "I don't even know if I said anything to her."
"And later, of course, you know, I find out who Pink is and I love her," he told Fallon. "And I just always felt bad because I hope she didn't think I was being rude or was not interested."