Carol. I mean, Ms. Burnett. I’m so glad we had this time together.

In the company of Carol, it’s easy to drop the formalities, the signifiers and the dignifiers. Even with you up there above our heads, rightly gracing the Mezzanine, Ms. Burnett, we feel as if we already know you. We collectively promise to stop short of the point of “creepy,” as opening speaker Tina Fey noted — as she herself humorously vacillated between the formal and the familiar, even quasi-curtsying between the complimentary punch lines. It’s just that we, Sunday night’s audience at the Kennedy Center, have spent so many hours watching you sing and yell, pirouette and pratfall, jump out windows and swan down spiral staircases — all in the name of laughter — that we feel we already know you so well, and so warmly.

Which is largely why this year’s Mark Twain Prize for American Humor ceremony, taped Sunday at the Center and scheduled to air on PBS Nov. 24 (check local listings), was about as good as you can do one of these lone-recipient awards shows.

It was funny. It was warm. And mostly, when it mattered, it felt authentic.

It’s been years since the Twain Prize nailed that mix so beautifully

Not for a long time at this ceremony — I’ve been attending since 2006 — has the event felt like such a high-level love-in. The night kept playing like a deft two-hander: On one hand, we had Ms. Burnett, the screen and stage legend who picked up the baton from friend/fellow comedienne Lucille Ball and continued to blaze trails. (When even current “Saturday Night Live” cast members are denigrating women comedians as less funny this month, it does us all good to be reminded of Ms. Burnett’s historic role.) And on the other hand, we had Carol, our reliable Saturday-night friend, the goofy/elegant first lady of variety.

Sure, there have been special Twain tributes before. In a word, I would describe Neil Simon’s year as “reverent”; Billy Crystal’s as “joyful”; Bill Cosby’s as “playful”; and the George Carlin event, just months after he died, was a “beatification.”

But in recent years, something was lost as the Twain took an interregnum from honoring comedy royalty, pivoting from legends to current superstars. Tina Fey, Will Ferrell and Ellen DeGeneres are all supremely gifted. Yet not only the politics of the thing grew awkward as the event began to honor midcareer talents; the temperature of the room changed when the memories being shared from the stage were not from last century, but rather last week. (The height of the onstage awkwardness may have come when Betty White joked, in tribute to Fey, that of course a comedian a half-century younger than the nonagenarian legend was picking up the prize.)

With Ms. Burnett — is anyone more deserving? — the Twain found its stride again. And it helped immensely that the casting approached an ideal.

There was the right representation of succeeding generations of actors/comedians. (Burnett is 79.) Fey, as the opener, was brilliant, hitting each fangirl beat, bouncing between wryness and respect.  And guest Martin Short — a master at mimicking Hollywood swarm and show-biz double-talk — heightened the sense of Burnett’s genuineness with a bit that spun the funny by invoking/mocking the usual award-show platitudes. And a third former “SNL”-er, Maya Rudolph, even drew knowing laughs with her “rendition” of Burnett’s sign-off song.

Burnett’s old variety-show cast mates Tim Conway and Vicki Lawrence unfurled their flawless comic timing, telling true stories (Lawrence) or adopting comic premises counter to Burnett’s generous reputation (Conway) that conveyed the love of her comedy peers.

Lucie Arnaz — whose family is longtime friends with Burnett’s — evoked how much Lucille Ball supported Burnett, and how much these two redheaded legends carried the standard for women in comedy.

And a serenading Tony Bennett and an anecdote-sharing Julie Andrews really classed up the joint. The elegant Andrews, in drawing on her 55-year friendship as “best chums” with Burnett, especially let us peek into the off-camera high jinks of Burnett — spotlighting our sense that Andrews is so very lucky, and that we all would cherish being Carol’s friend.

By the time Ms. Burnett — Carol — spoke, with humor and appreciation and self-deprecation, the love-in was complete.

And by the time she tugged on her left lobe — her old farewell trademark — the friendly legend tugged on our hearts. Yet it didn’t play as sappy or maudlin or overly sentimental. Like Carol herself delivering a punch line, it landed just right.

And the Twain had its best ceremony in years.