"If you were real fans, you'd be watching this on vinyl … Prepare yourself, Radiohead – you're about to meet Televisionface!"

With that introduction, Stephen Colbert's hour-long special of The Colbert Report featuring Radiohead ("presented by Dr Pepper, except for Radiohead who present themselves because they're nobody's corporate tool") began very much in the vein as it went on for the next hour, oscillating between genuine geeky fandom from Colbert the man, balanced against the comedy obligations of Colbert the conservative pundit persona.

Despite the Bill O'Reilly-esque character that he plays, Colbert has often used the Comedy Central show to indulge his very un O'Reilly-esque love of music and certain musicians. The Cars' Ric Ocasek has become a near-regular guest and, more recently, he did several shows with Jack White. But only Radiohead got a full hour, a first for the show itself, too.

"This is going to be a mindblowing event for the music nerds. So in the event, I have hipster paramedics standing by," said Colbert, pointing to a particularly sarcastic medic slumped to one side of the stage.

But despite the jokes, Colbert was sweetly visibly thrilled to have the generally interview-averse band on his show. But the band-members themselves looked even more thrilled to be there.

Thom Yorke in particular – not a man famed for his sense of humour – was clearly having the time of his life, being ribbed by the comedian and even making some jokes back.

"Why do Americans like you?" demanded Colbert.

"We don't know. Not a clue," replied Yorke, looking slyly out towards the audience.

When Colbert suggested it was just a hangover from Beatlemania, Yorke countered that they were "still waiting for the greeting off the plane with all the crowds and shit".

"Well, maybe if you were lovable moptops … but you guys have this totally indie ragged kind of quality."

Yorke burst into laughter while Jonny Greenwood behind him could barely sit up for giggling.

"How old are you?" continued Colbert. After some umming, Yorke, sporting a grizzled beard, replied that he is 42.

"Grow up, man," Colbert spat out. The band laughed delightedly.

Later when Colbert interviewed Yorke and Ed O'Brien about the band's commitment to the environment, Yorke managed to get in some digs about Rick Perry's eco-scepticism ("Let's say in order to be elected you need funds so you accept money from companies and some of those companies are oil companies") before giving it up for Colbert's comedy. When asked if Dr Pepper could ever become Radiohead's official soda, Yorke replied that it tasted like the stuff you swill in your mouth at the dentist.

"Well, it is a Dr," replied Colbert, much to Yorke's delight.

Otherwise, Yorke was in recognisably Yorke-ian form, from erring ever so slightly on the hectoring side when talking about the environment to twitching around in that now familiar way, like the man's never heard of self-consciousness, during the closing song The National Anthem.

That, along with the other three songs the band performed over the hour – The Daily Mail, Bloom and Little by Little – sounded nothing like what is generally played on late-night US talk shows, with more of an emphasis on haunting beauty than power rock ("Wowee!" cooed Colbert after Bloom.) Each performance was proof that a long relationship doesn't have to lead to fatigue and infighting for all bands but rather, in the case of Radiohead, tight, elegant and sympathetic performances. Not all of the songs were Radiohead classics (The Daily Mail, while a funny idea, barely touches its nigh on unmissable target) but they all – as is always the case with Radiohead – simply sound like nothing else.

And now it looks like the band might have one more unique quality: social consciousness but also a sense of humour.

"Who's better at saving the world, you guys or Bono?" asked Colbert.

Without even a pause, and looking the opposite of a tortured artist, Yorke replied, "Bono, definitely." And then he grinned at the audience one last time.