Wilco, Royal Festival Hall, London

For a few, most fortunate, bands, there comes a time in their existence when they are operating at such a peak of natural, instinctive power that everything they do seems just right.

It's like a state of grace: the songwriter picks exactly the right words, the drummer finds the perfect fill, the guitarist never hits a bum note, and most important of all, everything locks together with an easy, unforced precision, so it sounds like a single intelligence is in operation.

Some bands are lucky enough to get it straight away – The Ramones, the Pistols – while for others it's the product of years of hard graft. The Band were one such, honed through arduous road-time backing Ronnie Hawkins and Bob Dylan; another band with plenty of years on the clock, Wilco are currently in that state of grace.

As Tweedy sings in the opener "Wilco (the song)", from last year's career-defining Wilco (the album), the band offers "an aural arms open wide/ a sonic shoulder for you to cry on". The set is stuffed with emotional outpourings like "How to Fight Loneliness" and "I'm Always in Love" – the latter situation, typically, a source of worry to the fretful Tweedy. But despite the open-wound pain of some songs, there's a geniality about the band that is utterly engaging. They come on stage to the kind of corny music used to introduce guests on a chat-show, and insert cute individual spotlit introductions of the six band members into the stop-start conclusion of "Wilco (the song)" – simple, genius touches of ironic showbiz pizzazz that break the ice immediately.

Being unashamed rock classicists, there are plenty of echoes coursing through Wilco's songs: "I'm Always in Love" is a dead ringer for a Velvets chugging rocker, the unison guitar passages of "Impossible Germany" recall the Allmans in their prime, Nels Cline's little slide-guitar fill-ins on "You Never Know" are pure George Harrison, and there's even an element of an American John Lennon in Tweedy's languid nasal delivery. But it's the way they play with their influences that sets them apart from mere heritage rockers. There's nothing retro at all about the sonic architecture of "Via Chicago", in which the pleasant country-rock progress is suddenly sundered by manic drum-barrage bursts of musique concrète, through which Tweedy and co keep harmonising as if nothing untoward is happening. And the way that "Poor Places" shifts from lap-steel guitar and rattly percussion, sinking beneath a shroud of dark noise before re-emerging as the plaintive "Reservations", makes for the most daringly effected of segues.

Of course, it helps that they're all accomplished and imaginative players, working at the top of their game. The drummer Glenn Kotche may drive the band powerfully, but he's no mere time-keeper: sometimes wielding a mix of sticks and shakers, he inhabits these songs ingeniously, devising a detailed percussive topography that adds layers of meaning. The multi-instrumentalist Pat Sansone and the keyboardist Mikael Jorgensen likewise bring myriad details and textures into play.

The bassist John Stirratt has the playful melodic sense of a Rick Danko or Paul McCartney; and in Tweedy and Nels Cline, Wilco has perhaps the most innovative guitar-pairing of any mainstream rock band.