Pulp's ongoing renaissance has been one of the great pleasures of the last couple of years, but until now the USA – never a market that's been overly receptive to the band's charms, admittedly – has been left out of the party. So it's a thrill, albeit a belated one, to be finally seeing them on US soil at Radio City Music Hall tonight.

As with pretty much all Pulp's post-reunion shows, tonight's selection leans heavily on Different Class — 11 of the album's 12 tracks get an airing, with only 'Monday Morning' absent. That album's ubiquity is broken up with a couple of unexpected gems – 'Sunrise', from the unfairly maligned We Love Life, along with non-album tracks 'Razzamatazz' and 'Like a Friend' – with a couple of tracks from This Is Hardcore and His N Hers rounding out the setlist.

The immediate reaction is that it's hugely gratifying just to see Pulp on stage, with Jarvis Cocker throwing his idiosyncratic dance moves and gallivanting up and down the steps that led up to the balcony, while the band play as if the last decade or so never happened. During the breaks between songs, the singer breaks out his avuncular uncle routine – chatting with the megafan at the front who was at Pulp's last NYC show in 1998, passing out grapes and chocolate bars to the audience, discussing the origin of 'Babies' ("Only I know how much is true"), and quoting The Great Gatsby at length.

But once you get beyond the simple delight of at last hearing this music in a live setting (and a beautiful one at that), you start to think about why Pulp's music has aged so well. After all, nostalgia is a dangerous thing, and reunion tours rarely capture past glories. But this doesn't feel like a band ambling out to do the hits – these songs feel just as vital as they did 15 years ago, and Pulp feel just as relevant now as they did back in their, ahem, glory days.

It's perhaps because the songs and their subject matter are essentially timeless that this doesn't seem like an exercise in cheap '90s sentimentality. Only 'Sorted for E's and Wizz' seems somewhat incongruous, given how far removed Jarvis (and everyone else) is from the days of clandestine parties in Hampshire fields. But the likes of 'Mis-Shapes' and, of course, 'Common People', are as biting and relevant as they were 17 years ago, especially in a world where the working class is patronized more than ever.

There are others, of course, who've addressed such subject matter in the years that Pulp were scattered to the wind, but few who've done it so well. If this is the last time we see them in the USA, they'll be sorely missed. Again.