Jimmy Fallon and Jay Leno addressed the rumors of their rivalry, which stemmed from Fallon supposedly taking over The Tonight Show by the fall of 2014, when Leno's current contract expires.

Leno and Fallon sang the "Tonight" duet from West Side Story in a staged phone call between them, which bridged Leno's Tonight show to Fallon's Late Night. Fallon answers his iPhone when the caller ID says "Host of Tonight Show," and says, "Hey, Jay."

Leno says, "How're you holding up?"

Fallon: "Ok, I guess. You?"

Leno: "Yeah. I'll live. I've been through this before. Got to admit, I'm getting a little sick of this."

Then, the two launched into song, which was dubbed by professional singers at certain points. One of Fallon's lyrics says, "In the news, all they do, is say I'm replacing you, think they I can win the demo."

Leno: "Tonight, tonight, my ratings were all right. Twenty years and I'm still in first place."

Both: "Tonight, tonight, is it going to be Jimmy of Jay? Tonight, tonight, where will they tape "Tonight"? In New York, or will it stay in L.A.?"

"Why do they say we fight? I like you, you like me, we're OK."

However, Leno opened his monologue by saying, "Before we get started, let me say that NBC and I have reached a peaceful amicable agreement that will be beneficial to both sides. ...April Fools! It will never happen."

Rumors started that Fallon would succeed Leno when Jimmy Kimmel Live on rival network ABC started performing well in ratings. NBC feared that the rival ABC show would capture younger viewers, so talks began about Fallon taking over the seat of the Tonight Show. However, Leno continues to lead in the late shows, ahead of both Kimmel and Letterman on CBS.

If the skit proves anything, it isn't that Leno and Fallon are close friends; it's that they haven't lost their sense of humor over the future of the Tonight Show.

The pair sang, "Tonight, tonight, who cares who hosts 'Tonight'?"

"People just watch online the next day."