Set to the accordion, the fast-paced song condenses and lampoons the soundtrack from Miranda's wildly popular, Tony Award-winning musical.
Miranda, who was wearing a T-shirt with Yankovic's face emblazoned on it, said he was honored when he heard the satirist wanted to to write and record a Hamilton parody.
He added that when he finally got to hear the song, he had tears of joy streaming down his cheeks.
Miranda went on to say Questlove -- "The Tonight Show" music director -- called him immediately after he gave the song a listen and said: "Yooooooooooooo!' [Questlove] went: 'Forget your Pulitzer, your Genius Grant is nothing, you've been immortalized by Weird Al. You're done. You're done! You've peaked!'
"It's true!" Miranda agreed. "It's the greatest!"
The four men laughed and Questlove nodded to confirm Miranda's recollection of the events.
"You have to understand what an honor it is," Fallon told Yankovic, who smiled and hung his head in modesty.
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