Fallon is taking over hosting duties as Leno exits the late-night show Feb. 6, 2014.
In a skit accompanying Fallon's appearance on the "Tonight Show" Friday, Leno can be seen holding a pillow in preparation to smother the younger host as he napped.
"Jay, what are you doing?" Fallon asked as he woke up from his nap in the "Tonight Show" greenroom.
"I saw you resting," Leno said. "I wanted to bring you a pillow to make you more comfortable."
The two later came to mock blows when another guest, mentalist Lior Suchard, guessed Fallon's first kiss was with a girl named Megan when he was 11, The Hollywood Reporter said.
Leno got up from his chair, yelling at Fallon, "That bitch kissed you too?"