"My Time Of Day/I've Never Been In Love Before" also qualifies.
Nathan sincerely apologizing to Sarah for involving her in the bet and holding their gambling in her Mission.
Meta-example: Nathan Lane was born with the name Joseph Lane, but had to change it when he became an actor because another actor already had that name. He chose the first name "Nathan" because he had always wanted to play Nathan Detroit. In 1992, he got his chance (and a Tony Award nomination) when the musical was revived on Broadway.
another meta-example: despite Jean Simmons being the third choice for Sarah Brown (see Trivia), studio exec Sam Goldwyn was so impressed by her performance after seeing the rushes, that he was heard to say "I'm so happy I couldn't get Grace Kelly."
Despite successfully taking Sarah to Havana, Sky tells everyone that he lost the bet and pays up the thousand dollars to Nathan Detroit. Sarah finds out about the bet from Nathan later.
And the way Nathan tells Sarah, at least in the stage version, also avoids hurting her feelings or getting her in trouble with the people at her mission. While giving testament at the mission, Nathan admits to betting "a certain guy could take a certain doll with him to Havana," and also admits it was wrong of him to get the doll in question involved, and says all this while looking directly at Sarah, obviously trying to apologize to her. The look on her face makes it clear all is forgiven. He then says there was no harm done, as he won the bet — "The guy told me he didn't take the doll." And that's what gets Sarah to realize Sky really does care about her.
The kicker is that, depending on how it's staged, this can very easily come off as Nathan knowing perfectly well that Sky won, but also knowing he lied to protect Sarah, and is cluing her in so the crazy kids can finally get together. And, of course, They Do.