This anecdote is also from the Tynan New Yorker profile. I remember liking it a lot.

Example of Carson when the spirit of pure, eccentric play descends upon him and he obeys its bidding, wherever it may lead: During the monologue on May 11, 1977, he finds, as sometimes happens, that certain words are emerging from his mouth in slightly garbled form. He wrinkles his brow in mock alarm, shrugs, and presses on to the next sentence: “Yetserday, U.S. Steel announced. . .” He pauses, realizing what he has said, turns quizzically to McMahon, and observes, “‘Yesterday’ is not a hard word to say.” Facing the camera again, he goes on, “Yesterday—all my troubles seemed so far away . . .” Only now he is singing—singing, unaccompanied, the celebrated standard by John Lennon and Paul McCartney: “Now it looks as though they’re here to stay. Oh, I believe in yesterday.” By this time, the band, which was clearly taken by surprise, has begun to join in, at first raggedly but soon improvising a respectable accompaniment. Warming to his berserk task, Carson does not stop until he has reached the end of the chorus. He resumes the monologue: “Now, what was I talking about? Oh, yes. Yesterday . . .” But no sooner has the word passed his lips than Doc’s combo, determined not to let him off the hook, strikes up the melody again. Undaunted, Carson plunges into the second chorus. Having completed it, he silences the musicians with a karate chop. There is loud applause, followed by an extended pause. Where can he go from here? Cautiously feeling his way, he continues, “about twelve hours ago, U.S. Steel announced . . .” And successfully finishes the gag. Everyone in the studio is laughing, not so much at the joke as at the sight of Carson on the wing. Grinning, he addresses McMahon.

Carson: That’s what makes this job what it is.

McMahon: What is it?

Carson: (frowning, genuinely puzzled): I don’t know.

Gorgeous.