Muse, The Den, Teignmouth

Seaside Special was never like this: two Mr Punches leer over the stage from posters either side, a circus ringmaster opens proceedings, yet big-top glitter and knockabout humour are way off the agenda.

This thrilling power trio have faced down local opposition to devise a high-profile return for their first hometown gig since 1995, an odd move given how quickly Muse first escaped, then complained about this Devon resort.

Yet even outsiders need to prove themselves, so the band have sought to realise a teen fantasy of playing the sward that runs between the beach and Teignmouth's once elegant townhouses. Yet playing to 20,000 fans over two nights is small beer for a group whose last album, 2007's Black Holes & Revelations, debuted at number one and led to their headlining the refurbished Wembley Stadium.

On their follow up, The Resistance, due out next week, frontman Matt Bellamy gives full vent to his paranoid concerns about global conspiracies and 1984-style state control, backed by Muse's most rococo compositions to date, including full orchestra and even a three-part suite. Nowadays just as likely to appear in tabloid columns as music journals, Muse are aware of their kudos and flex their muscles accordingly. Yet behind the proud swagger as they take the stage, there are glimpses of the awkward kids who never fitted in.

All Bellamy can manage by way of explanation is wry understatement – "It's been a very long time indeed"– while bandmate Dominic Howard looks uncomfortable standing on his drum stool to explain that tonight is a dream come true. Only in performance do Muse emerge as one of our most uninhibited bands. From the Goldfrapp-meets-Glitter Band stomp of their opening gambit, new single "Uprising", the threesome prove their ability to polish rock's most recognisable tropes with a futurist sheen. The album's dark title track is Bellamy's clearest explication to date of a key theme that emerged on their last album – the power of love to defeat the ill-defined "Them" who crop up throughout The Resistance.

While these numbers hit hard with sudden immediacy, "United States Of Eurasia" baffles at first. It is a national anti-anthem that Bellamy begins quietly at the piano, crooning "We know there's no one we can trust", before the "We Are The Champions" refrain kicks in. The terse "Unnatural Selection", meanwhile, sounds too earnest without the band's usual flamboyance, though it is contemporary R&B that proves a step too far for both the band and their fans. Electronic drums pulse and synthesised strings pluck incessantly throughout "Undisclosed Desires", with some slap bass from Chris Wolstenholme, but it lacks the snap of Timbaland's finest and the smattering of polite applause at its close is the outdoor-arena equivalent of tumbleweed.

It is frustrating, for Muse often run seamlessly on dance beats, as they prove tonight with a lubricious "Supermassive Black Hole". Certainly, they benefit from enough formidable craft to make up for the occasional lapse. As master of ceremonies, Bellamy marshals a bewildering array of guitar effects, from the metallic crunch of "Hysteria" to the intensity of "New Born", where he judiciously introduces his falsetto.

Another rare false note is their straight cover of quirky synth instrumental "Popcorn", where they act like a comedic uncle trying too hard to be wacky. Better is their introduction of "the oldest song we know", "Cave", from debut album Showbiz. Bellamy replaces its angsty guitar with jaunty piano, but he fails to disguise the youthful alienation when he warns, "So come in my cave/And I'll burn your heart away".

Then again, it is a refuge that Bellamy left long ago, as is clear when they close with the archly delivered pomp and defiance of "Knights of Cydonia". Against them, resistance is futile.