That Robert Smith: he wafts onstage looking like he couldn’t knock down fairy floss but the man has chutzpah to burn. Deep cuts, we were promised, even B-sides, to go along with the hallowed and multimillion-selling album Disintegration, performed in sequence. But who on earth plays the rarities first? The Cure, that’s who. I’d been thinking – given that The Cure are not known for shows that run shorter than three hours – maybe they’ll play “Lament”, a perfect icicle of melancholy that first appeared in 1982, and has rarely been performed since. Or “Splintered In Her Head”, a B-side from 1981, which sounds like birds beating their wings inside a dank cave. I thought my speculations made me clever. I was confident of being a True Fan. I wasn’t thinking of an unreleased demo called “Delirious Night” – a rough mix of which is buried on the second disc of a deluxe reissue of Disintegration from 10 years back – but they open the show with it. I hadn’t given a moment’s thought to “Esten”, another Disintegration-era demo that conveys glimmering sadness the way only The Cure can, but which never got finished enough to have a vocal. They play it, too. Outdone in obscurantist Cure knowledge by The Cure: reader, I had not expected this.

And then, having flummoxed us for just a little while, The Cure take an intermission. Well. Let’s grab the chance to talk Disintegration while they’re gone – saves us complaining about this shoddy set design. You call these spiderwebs, sirs, draping the stage? I’ve seen lies better spun.

Disintegration was The Cure’s eighth studio album, released 30 years ago this May. It’s more than 70 minutes long and feels it, vast and deep and dark, its atmosphere the consequence of Smith having a meltdown at the prospect of turning 30 and deciding to nurse himself through it with hallucinogens and just a touch of creative hubris. It’s easy in this respect to think of Disintegration as a solo album in all but name – it’s Smith’s face alone that graces the cover – but this overlooks its potency as a document of a band who knew how to play the songs with the right mixture of sorrow and petulance. I think the title track is about someone deciding to have an affair and then changing their mind but feeling walled in by boredom, regardless. You know who else gets irascible, bored and depressed? Teenagers, which helps explain why two if not three generations of them have clung to this album written by a married and despondent 29-year-old. Who is now 60. My, would you look at the time.

Ah, they’re back again. Stage left to right: Roger O’Donnell, keyboards; Jason Cooper, drums; Robert Smith, genius loci; Reeves Gabrels, guitar. Simon Gallup, bass, is a perpetual roamer and therefore the only right counterfoil to his singer, who prefers to stand as rooted as a tree. Smith says that if Gallup were to ever leave, the group “wouldn’t be called The Cure”, but it’s not just Gallup’s playing that makes a Cure song a Cure song. The fact that only three of the musicians who recorded Disintegration are the same ones who are onstage – Smith, Gallup and O’Donnell – matters more than anyone in The Cure’s current line-up would probably wish to admit.

Disintegration turned The Cure into a stadium-sized band, which had not been their intention. Bands that routinely play at such a scale tend to slough off all their subtleties, but these songs, made up of contrapuntal melodies and spiralling rhythms, benefit from being played with delicacy as much as force. The heart-aching “Pictures of You”, for instance, which is threaded through – or should be – with Smith’s silvery, reverberant guitar lines. Or “Lovesong”, The Cure’s unlikely chart hit, with its minor-key plangency and Gallup’s bass hesitantly carrying the tune. Rarely has a song about true romance sounded so ambivalent. It’s these sort of shadings that are missing this evening, partly sucked away into the Concert Hall’s endless roof cavity, partly absent because of who’s playing.

Gabrels – who worked with David Bowie for many years – has a blunt and abrasive style at odds with much of this music, and, despite having been a Cure member since 2012, he still has the air of a hired hand. O’Donnell, too, an on-and-off Cure member, doesn’t seem wholly committed, which means both onstage flanks are wanting. Because of this, the songs that end up working best are the ones where less can be more: a magnificent, stately “Last Dance”; a squalling run through “Disintegration” that tests Smith’s vocal ability – he wrote it in a key too high for his range, for the anguish it would add – but which he pulls off by dint of will. I don’t think Smith has ever phoned it in, and his everlasting sincerity – flavoured with a sharp speck of mischief – is the answer to the question of how and why The Cure keep going and going.

And yet, against all expectation, this is a short show by Cure standards: two hours and change. I can’t have been the only one anticipating multiple encores, an adventure through the back catalogue. Instead, all we get after Disintegration winds to a close with “Untitled” – the most honest thing that Smith has ever written – is three songs. One of them is “Three Imaginary Boys”, the dream-like title track to The Cure’s 1979 debut album, and trust Smith to say, as he does here, that “I’m the only one who thinks Disintegration is getting too much attention.” After 40 years at this it still seems to surprise him just how fiercely he is loved. The whole crowd is on their feet. I think of “2 Late”, the B-side to “Lovesong”, which was played early tonight. “So I’ll wait for you / Where I always wait,” Smith sings, at the outset, and it momentarily overwhelmed me, to recollect how much time I’ve spent with The Cure, time I’ll never get back.

The final show of The Cure’s Disintegration 30^th anniversary at The Sydney Opera House is on May 30.