"I was singing, and I was in the middle of a very, very iconic song — which I don't want to give away — and I saw someone walk in, and I could feel the energy in the room sort of change."

Milioti said that without her glasses, she wasn't able to tell that it was Bowie who had walked into the rehearsal room. She squinted at him and thought, "I don't know who that is, I'll just keep singing...Should someone check if he's supposed to be here? Not sure."

Host Meyers replied that Bowie likely thought, "She is big time — she iced me."

Meyers also commented on the fact that Milioti would not reveal the song she was singing, bringing to light how the show has been "shrouded in secrecy."

"We don't talk about it because it's meant to be experienced," Milioti responded. "It's very much in David Bowie's world and Ivo's [van Hove] world and Enda, and it's out there and it's an art theatre piece." "You were saying backstage that this will be a show that is guaranteed to be divisive. People will love it, people will hate it," Meyers continued.

"It is very divisive," Milioti confirmed. "And it's very freeing. I like that."

Watch the full interview below:

New York Theatre Workshop's production of Lazarus, written by Tony winner Walsh with music by Bowie, is inspired by Walter Tevis' best-selling 1963 novel "The Man Who Fell to Earth," about a human-looking alien who comes to Earth seeking a way to bring water back to his dying home planet. It was also adapted into a film in 1976 starring Bowie in the lead role of Thomas Newton.

Along with Milioti, the show stars Michael C. Hall ("Dexter," Hedwig) and The Last Ship's Michael Esper.

As previously reported, the musical is NYTW's fastest-selling production in the company's history. It sold out its initial engagement in just three hours, prompting a three-week extension. Performances will now run Nov. 18-Jan. 17, 2016. For more information, visit NYTW.