Wilco, Forum, London

Where you been?" responds an amused Jeff Tweedy to a punter's call to "play the hits", midway through Wednesday's show at the Forum. "These are the hits!"

You can understand the punter's (surely ironic) point: Tweedy's band, Wilco, all but exemplify the unnamed outfit referred to in his song "The Late Greats", about a fantastic rock group whose music never gets played on the radio. That's no longer the case with Wilco, but they remain something of a cult favourite, albeit a cult large enough to pack out the Forum.

A handful of songs further into the set, Tweedy engages the audience in some mild banter about whether American or British crowds are better at singing along, and leaves the lovely "Jesus, Etc", from their top-selling Yankee Hotel Foxtrot album, to be sung entirely by the fans. The result, underscored with mellotron and lap steel guitar, is word-perfect and indefinably moving, as charming and poignant a moment as I've experienced at any concert this year.

After opening with "Ashes of American Flags", the set gets into its stride with "Bull Black Nova", from this year's Wilco (the album). The three guitars itch away, bursting into intertwining lines reminiscent of old psychedelicists such as Quicksilver Messenger Service, then fragmenting into avant-rock noise which recalls the late New York guitar legend Robert Quine.

It's a thrilling sound which seems to yoke together the styles and histories of East and West Coast American music, culminating in all three guitarists pawing the stage, heads down, in classic Neil Young mode. It is impossible not to acknowledge that Wilco are the Great American Band of their era.

It's also impossible not to marvel at what Nels Cline has brought to the band. Whether wresting ungodly noises from a Fender Jazzmaster or stroking gentle colouration from a lap steel, his contributions are quite extraordinary. As he stalks and stomps about his corner of the stage, scattering beautiful, aberrant noise in his wake, I'm not the only one reminded of Radiohead's Jonny Greenwood.

Cline is perfectly suited to Wilco, his vast knowledge of guitar modes from rock and country to free jazz helping ease the stylistic transitions that have become an important aspect of Tweedy's songs. On one level, this means a song such as "At Least That's What You Said" can slip gears smoothly between a quietly intimate opening and a full-on, guitar-mangling conclusion. But the band's embrace of populist and avant-garde methods also enables them to effect more devastating sonic coups, such as the huge swell of drum and noise barrage which suddenly overwhelms the plaintive "Via Chicago" mid-song while Tweedy sings along regardless, like a passenger left behind in the departure lounge, wanly watching as his plane takes off. It's a perfect example of how Tweedy renders tender personal emotions within dauntingly large-scale distractions.

Wilco are so good, the audience won't let them stop. "Via Chicago" is followed by a second encore of the lengthy "Spiders (Kidsmoke)", a chugging variation on the great Neu! motorik groove laced around with all manner of guitar-noise from Cline and Tweedy. The crowd demands more. The band return for three deliriously received numbers – among them "The Late Greats" and "Heavy Metal Drummer", which aptly celebrate the bonds between rock bands and their fans – and are about to embark on a fourth when either a curfew or an electrical problem prevents them. Undeterred, Tweedy grabs an acoustic guitar, steps to the lip of the stage and sings "Someone Else's Song" without a microphone. It is a magical, moving conclusion to one of the best gigs of the year, by one of the best bands in the world.