"She was the best audience, she was the one I was always trying to make laugh", he said.
The chat show host said he was greatly appreciative of the support he and his family received during such a hard time.
While singing "New Year's Day", Swift delivered a lyric which paraphrases Fallon's tender story - "Squeeze my hand three times in the back of the taxi".
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"Last week I was in the hospital and I grabbed her hand and squeezed "I love you" and I just knew we were in trouble", he said.
Watch Jimmy Fallon's tribute above.
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Jimmy - whose comeback show also featured a surprise performance from Taylor Swift - said: "Mom, I'll never stop trying to make you laugh".
The singer, 27, performed her new single "New Year's Day" while playing the piano following the late night host's monologue.
Of the emotional performance, he said, "I almost gasped".
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There were special performances by Melanie C, Alfie Boe & Natalie Lowe, Emeli Sande and others all in tribute to the armed forces. Prince Charles will lead the annual ceremony at the Cenotaph in London and Big Ben will chime at 11:00 GMT.
Tonight Show writer and producer Mike DiCenzo took to Twitter for some background on Swift's performance and the emotions she wrought. "Tears. I think everyone in the audience started sobbing", he wrote. It was a lovely coincidence in a handsome performance. "She would squeeze my hand three times and say, 'I love you.' And I would squeeze back, 'I love you, too, '" he said. "'Hold on to your memories, they will hold on to you, ' Taylor sang".