RBG Meets Her 'Star Struck' 'SNL' Performer Kate McKinnon in 'Adorable' Run-in at New York City Musical

"Kate got up at one point from her seat and shook Ruth's hand," says a source, adding, "She was overjoyed"

Ruth Bader Ginsburg meet … Ruth Bader Ginsburg!

The Supreme Court justice ran into Saturday Night Live‘s Kate McKinnon — who famously plays Ginsburg as a feisty sprite with a stand-up’s spirit, no larger than a flea and sharper than a razor blade — when the two attended an off-Broadway performance of Fiddler on the Roof on Tuesday night, PEOPLE confirms.

“Both were incredibly gracious and kind,” a source at the scene tells PEOPLE, noting the women “raved about how much they loved the show.”

McKinnon “was star struck,” according to Fiddler actor Nick Raynor, who recorded part of their meeting in a video later shared on Twitter.

The all-Yiddish production is directed by Joel Grey, who joined Ginsburg, 86, and McKinnon, 35, on stage after the show, the source says. They also met and posed for photos with cast and crew.

Jeff Spicer/Getty; Michael Kovac/Getty

“Ruth and Kate both came into the house right before the curtain rose for Act 1, so not a lot of people noticed,” the source explains. “But at intermission, word spread with the crowd and they went crazy for her, giving her a standing ovation after she came back from the bathroom. Someone even shouted ‘Rock on Ruth!’ It was electrifying.”

“These two incredible women — it could not have made me happier,” Grey, 87, tells PEOPLE. Ginsburg, whom he says he last saw at a friend’s son’s bar mitzvah a few years ago, “was generous and sweet. The audience went crazy for her.”

From left: Joel Grey and Kate McKinnon. Tricia Baron

Actress Jodi Snyder, who appears in the musical, shared on Instagram that Ginsburg’s ovation lasted two minutes.

“Ruth was so gracious, smiling, waving and shaking hands with fans,” says the source there on Tuesday. “Kate got up at one point from her seat and shook Ruth’s hand, too. She was overjoyed and was cheering Ruth on with the rest of the crowd. It was adorable.”

While she took pictures afterward with the cast and crew, “Every stage hand was there,” Grey says. “You’ve never seen happier faces on 50 people.” (Both Ginsburg and McKinnon were “thrilled and moved, it’s that kind of show,” he says, “Especially in these times.”)

Kate McKinnon as Ruth Bader Ginsburg on Saturday Night Live. Will Heath/NBC/NBCU Photo Bank via Getty

McKinnon, who has been with SNL since 2012, has played Ginsburg since that year.

Though the long-serving justice, who leads the court’s liberal wing, has said it’s not an exact impression, McKinnon’s version tickles her nonetheless. She watched some of McKinnon’s sketches during filming for RBG, a documentary about her life, where she called McKinnon “marvelously funny” if “not one bit” like her.

Asked about it last year, while doing press for the RBG premiere, Ginsburg said, “I liked the actress who portrayed me.”

And then, perhaps channeling a bit of McKinnon’s version of herself, Ginsburg added: “And I would like to say ‘Gins-burn’ sometimes to my colleagues.”

Updated by Liz McNeil