The star was singing the track New Year’s Day from her latest album Reputation, which came out last week.
It was a surprise performance, and one that was booked-in at the very last moment.
Last night’s episode of The Tonight Show was Fallon’s first since the death of his mother – and DiCenzo has revealed just why New Year’s Day struck a chord with him, and left him visibly emotional at the end of the track.
The episode began with Fallon revealing that when he was a child, his mother would “squeeze my hand three times, and say ‘I love you’.
“Last week, I was in the hospital and I grabbed her hand and squeezed ‘I love you’. I just knew we were in trouble.”
Sure enough, that anecdote ended up having similarities with Swift’s song.
DiCenzo tweeted: “[Swift] was not scheduled to do our show today. But we wanted something special for this first show back, so we asked her on a complete whim, since she had been in town doing SNL. She said yes with zero hesitation.
“She sang New Year’s Day. No one had heard it. Suddenly she sings the line, ‘Squeeze my hand 3 times in the back of the taxi.’ I nearly gasped. Tears. I think everyone in the audience started sobbing.
“I could see Jimmy silhouetted at his desk dabbing his eyes with a tissue. We all lost it. It was a beautiful coincidence in a beautiful performance. ‘Hold on to your memories, they will hold on to you,’ Taylor sang.
“That hug between Jimmy and Taylor after the song was 100% real emotion. Whatever you think of Taylor, she did something beautiful for Jimmy and our show today, and we’re forever grateful.”
The performance has already had over 300,000 views on YouTube in less than 12 hours since being uploaded.
Reputation by Taylor Swift is out now.