She was the one I was always trying to make laugh.
Fallon canceled "Tonight" on November 3, when his 68-year-old mother fell ill.
At one point she changed the lyrics of "New Year's Day", a track from her new album Reputation, to say, "Squeeze my hand three times in the back of the taxi".
He went on to thank fans for all the support he and his family had received since his mother's death. "I just knew we were in trouble, you know?" he said through tears.
The presenter said everyone at the show would "continue to work really hard to bring some light and some laughter into the world".
"Our hearts go out to Jimmy and everyone else whose lives were so touched by Gloria Fallon's love, kindness and support", the network added last week.
"Mom, I will never stop trying to make you laugh", Fallon concluded.
Swift, whose new album Reputation dropped last Friday and is charging to the chart summit in the USA, United Kingdom and in markets around the globe, stopped by the Tonight Show studios Monday evening to dish out some music therapy: a performance of "New Year's Day".
Of the emotional performance, he said, "I almost gasped".
"Tonight Show" writer and producer Mike DiCenzo offered some insight into Swift's appearance on Twitter, explaining that she was not scheduled to perform, but the crew wanted to do something special for Fallon, and Swift quickly got on board. Tears. I think everyone in the audience started sobbing. We all lost it. "'Hold on to your memories, they will hold on to you, ' Taylor sang".