Taylor Swift appeared to bring Jimmy Fallon to tears with the power of her voice and her keyboard during a recent Tonight Show performance – but according to one producer, the reason for Fallon's emotion was much more complex.

Swift performed on Fallon’s show shortly after his mother, Gloria, passed away. The show was Fallon’s first since his mother’s death, and he opened it with a heartfelt tribute.

“[My mother] was the best audience,” he said. “She was always the one I was trying to make laugh, because she was such a fan of the show, and everything I did.”

He told the audience about how, when he was a child, his mom would squeeze his hands three times to signify: “I love you.”

“Last week I was in the hospital and I just grabbed her hand and squeezed: ‘I love you’,” Fallon said, beginning to tear up. “I just knew we were in trouble.”

Ms Fallon passed away on 4 November, at the age of 68.

According to tweets from Mike DiCenzo, a writer and producer on Fallon’s show, the crew wanted to do something special for the host on his first day back.

They contacted Swift, who was in town for an appearance on Saturday Night Live. The singer agreed to perform on Fallon’s show with “zero hesitation,” Mr DiCenzo said.

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Swift debuted the song “New Year’s Day” off of her new album, Reputation, in an acoustic performance on Monday night. The song, which was released along with the album only days before, is presumably about a couple sticking together through difficult times. But the mellow number also includes the line: “You squeeze my hand three times in the back of the taxi.”

Mr DiCenzo said none of the crew members had heard the song before, and were shocked by the resonance of the lyrics.

“I could see Jimmy silhouetted at his desk dabbing his eyes with a tissue,” he said. “We all lost it. It was a beautiful coincidence in a beautiful performance.”

Questlove, the leader of the Tonight Show’s house band, expressed his surprise on Twitter, writing: “I’m just realizing Taylor didn’t readjust the song’s lyrics for tonight’s performance. … Wow. You can’t plan these things.”

After the performance, Swift quickly stood up and embraced Fallon. The hug, Mr DiCenzo said, was “100% real emotion”.