Adam Smith is the first to admit that his debut feature film is not the easiest sell in the history of cinema. "There's no real narrative strand," says the director. "It's 85 minutes long, it's got paintballs exploding – and clowns. I was saying to someone the other day, 'You'd never commission it, would you?'" He laughs. "It sounds rubbish, you know?"

Seated across the table from Smith in a west London pub, Tom Rowlands, one half of the Chemical Brothers, frowns. "There is," he says heavily, "some music in it is as well." But even taking into account the film's subject matter – the Chemical Brothers headlining Fuji Rock festival in Niigata, Japan, last year – Don't Think still seems on the face of it an unlikely candidate for cinematic glory. "It's quite a singular experience," admits Rowlands. "It's an hour and a half of …" He searches for the right word to describe the ferocious electronic psychedelia of the duo's live set. "Bosh," he decides, adding that the film has no scene-setting introduction, "just a load of cutlery falling in slow motion."

The duo have previously proved resistant to being filmed on stage. As Ed Simons, the other half of the Chemical Brothers, puts it: "You play live because you want people to see it and have a good time – and cameras create an obstacle to really being in the moment." What's more, the concert footage was all shot on one night, which, says Rowlands, is not the way such films are usually made. "You shoot five nights and wear the same clothes every night, then chose the best bits," he says. "But this all hinged on one show. It could have been disastrous: some nights the screens behind us didn't work, or the visuals went out of time with the music. If that had happened, there was no going back."

Smith nods. "Don't Think was definitely the right title." At least, he says, the slightly chaotic approach was in the spirit of his long-standing collaboration with the Chemical Brothers, which began at their first live performance in the early 1990s. Asked by DJ Andy Weatherall to appear at his London club, the duo were too nervous to appear on stage, playing in "a cubby-hole above the cloakrooms" while Smith projected slides on to the empty stage; at a later gig, at Brixton Academy, Smith ran 16 projectors off a Hornby train set's power pack, an experience he cheerfully describes as "hellish". Rowlands adds: "We were using broken synthesisers, things that had been outmoded by digital technology; and Adam and his partner were doing a similar thing with their projections, refusing to do them on video."

Both parties have clearly moved on from those days. Smith has directed episodes of Doctor Who as well as the BBC's 2008 Little Dorrit, while the Chemical Brothers have sold millions of records, won umpteen awards (most recently the Los Angeles Film Critics' gong for their soundtrack to the 2011 thriller Hanna), and had an album buried in a time capsule in the Blue Peter garden. The duo also plan to collaborate with Smith on his forthcoming film version of Dope Girls, Marek Kohn's remarkable history of interwar narcotics scares and scandals, subtitled The Birth of the British Drug Underground.

There have been great concert films – Martin Scorsese's The Last Waltz for the Band, and Jonathan Demme's Stop Making Sense for Talking Heads – but for the most part, they tend to exist as minor add-ons to artists' careers, something knocked together and bunged out on DVD for the diehard fan. What's noticeable about Don't Think, though, is the sense of risk-taking that pervades it. And the film has thus far received near-blanket acclaim. One critic evoked the concept of "pure cinema", a phrase that places it in the same grand tradition as Dziga Vertov's classic 1929 silent documentary The Man with the Movie Camera and Leni Riefenstahl's 1938 Olympia. Another offered a more prosaic assessment: "It made me want to take loads of drugs."

Certainly, there's something dazzling about the band's live show, based around vast projections of the vivid films Smith made to accompany their 2010 album, Further; along with all the clowns and the paintballs, these feature starlings circling Brighton's ruined West Pier, an animation of a rearing horse influenced by Italian futurist painting, and clips of actor Romola Garai, of The Hour fame, diving into a swimming pool in slow motion.

Combined with the Chemical Brothers' music, it makes for an intense, exhausting experience. "Sometimes after gigs this year," says Simons, "I'd notice at the end that people looked a bit overwhelmed. It was a mystery to me: I used to wonder why people were just hands-in-the-air, this-is-brilliant all the way through. But now, having seen a gig – you're exposed to quite a lot, aren't you? All the imagery, the sound, it's a lot to take in."

There's also something rather moving about the way the camera keeps switching to show the two unassuming figures at the centre of Don't Think: these shots of the Chemical Brothers have a strange intimacy, capturing the closeness of a relationship that began almost 25 years ago at Manchester University. "When you're up there," says Simons, "you think the whole world can see you. You think everyone's vibing off you, but people can't really see you at all. People who've seen us live loads of times have come up to us afterwards going, 'Oh, I didn't know you were having such a good time up there.' Which is a bit deflating, really. "

But the real strength of Don't Think lies in the way it captures the band's audience. The film continually turns its focus away from the stage, at one point following a member of the crowd who wanders off to get food and meet friends, with the music still thundering away in the background. "I love the bit where the camera walks away," says Simons. "It's not so reverential. You know, I can be at a festival, watching a band, really into it, but I'm still thinking, 'I wonder what I'm going to eat later?' However much you love a band, there's always a little bit of your brain buzzing around other things, and I like that it captures that – all the randomness that goes with being in an audience. It's not just about 'I really love this band, I really love their music', because no one is actually like that."

Even more striking is the way the film keeps showing individual members of the crowd, bathed in coloured lights, behaving in a remarkably unselfconscious way, as if completely unaware of the cameras; it's the opposite of the kind of drugged-up, hello-mum gurning you tend to get when someone films the audience at a rave or festival. "One of our big things was how you do a concert film that emotionally connects," says Smith. "The audience were incredibly accommodating. We put little signs up with messages in Japanese saying, 'Please don't look in the lens if you're being filmed, just watch the show.'"

Some of the footage was taken by a team of four amateurs, out and about in the crowd armed with small cameras. "They could shoot really well but it wasn't their full-time job," says Smith. "One was the assistant editor, another was the girlfriend of the guy who operates the lights. They're all really nice people; they don't have that 'I'm a cameraman, can you do that again?' thing. It's like great portraiture: it's about a relationship, a trust."

The result has a fair claim to be called one of the best films about dance music ever made. You could argue that Don't Think's colour-saturated footage tells you more about the actual experience of the genre than any number of interviews could ever hope to. Whatever Smith's methods, he has succeeded in catching the one thing that has proved elusive to film-makers, despite all the documentaries and dramas that have been devoted to the subject since the acid house summer of love in 1988: the moment of what you might call dancefloor transcendence – when, as Simons puts it, "you're lost in it". "He managed to get the emotion of it," says Rowlands, "which is difficult to get across, because there's something intangible about it."

This may explain why it's fairly easy to reel off the many films and TV shows that got dance music and drugs disastrously wrong (from the Inspector Morse episode involving a new killer rave drug to the jaw-dropping 1996 film Vibrations, which contains the unforgettable line: "We're on a journey to sonic grooviness!"). The ones that get it right are noticeably harder to list.

"I don't really think people get that absorbed in music at the moment," says Simons. "They're streaming it, they're watching YouTube clips. People say 'I listened to this' and you think 'Yeah, did you listen to it on computer speakers?' I've had lots of tweets, people going, 'What am I meant to do when I go and see Don't Think? Am I allowed to dance in the cinema?'"

He laughs. "Well, you can if you want. But I just like the idea of people listening to our music quite loud."

• Don't Think will be at selected cinemas worldwide from 1 February. Details: dontthinkmovie.com