Anna Wintour isn’t the type of person best suited to endure the charade that opens each interview on “The Colbert Report.” After introducing the guest, the host takes a victory lap and applause from the crowd night after night, leaving the esteemed visitor in the shadows. There’s no one in the world of fashion that could pull such a stunt and get away with it, even if they adopt something like Stephen Colbert’s wink.

Yet, there was Wintour on Wednesday night, sitting in that star-spangled studio, as Colbert hammed it up. And she was smiling, her eyes unblocked by those by those ubiquitous black Chanel shades. The visit was a chance to talk about “Impossible Conversations: Schiaparelli and Prada,” the exhibition at the Met that had its debut with a modest little party Monday night.

The two of them got chatty.

Wintour: A designer like Miuccia Prada, she’s going far deeper than just simply things that you put on your back. She’s examining things that are happening in the world through art, through film, through music, and that’s really what this exhibition is really trying to talk about.

Colbert: Well, I don't really trust Prada.

Wintour: Well you’re wro— 

Colbert: Because my understanding is, the devil wears Prada. And this is a Christian nation, madam!

Wintour: That movie was so last year.

It’s no surprise that Wintour can ably deflect such jabs — when she attended a screening of “The Devil Wears Prada,” she chose an outfit from that very fashion house. She’s in that jocular mode for the entire interview. When Colbert brings up batter-friend shrimp at Long John Silvers, Wintour suggest they go there and have some, on a date. And she’s quick to make fun of Colbert’s clothing.

This charming disposition, is it a front? It’s not the Nuclear Wintour image forever put forth in magazine profiles, documentaries and, yes, Hollywood blockbusters. But Wintour has to do more than your usual editor-in-chief face time on talk shows and panels. She oversees the Costume Institute Gala, of course, but it’s more than just a party. Last year’s “Alexander McQueen: Savage Beauty” was the best-attended exhibition in the history of the Metropolitan Museum of Art. Also, she convinced Mayor Bloomberg to support Fashion’s Night Out, which will occur in more than 20 countries this September.

And these are part of her position in the fashion world, where she moves the chess pieces in a way that’s impressive even for someone at the top of the masthead at Conde Nast. David Remnick sits on the board of the New York Public Library, but he can’t operate within the world of arts and letters in the same way that Wintour moves within the world of the runway.

So, these projects may be the reason we see a surprisingly sunny Wintour sitting opposite a mock-jingoistic Colbert. But the audience members who cheer for Colbert’s right-wing parody every night switched allegiances at one point in the interview. Asked about Barack Obama’s support of gay marriage, Wintour says, “I am thrilled. There were tears in the office at Vogue today in the support of gay marriage. We’re thrilled about the president.” After a moment of uncertainty, wondering whether to break the show’s jokey conceit, the audience bursts into applause. This time, they are clapping for Wintour.