Production sources tell us Ariana was scheduled to appear on "The Tonight Show Starring Jimmy Fallon" Thursday ... but she was only going to do a comedy skit. She was not going to sing.

When she arrived on set, producers asked her if she would perform an Aretha song in honor of the late singer. Ariana told them she couldn't do it ... she was just too emotional in the wake of her death. She said Aretha was one of her heroes.

We're told Questlove then approached Ariana and convinced her it would be awesome for her to perform an Aretha song with the Roots.

Ariana changed her mind and opened the show with 'Natural Woman.' It's the first thing you'll see if you watch the show. Ariana brought the house down and got a standing O.

We're told when Ariana left the stage she broke down in tears.