This week, the website Fusion published a timeline lamenting “How Art Basel Miami Beach became one big party”. The penultimate entry was Miley Cyrus being invited to play the gallerist Jeffrey Dietch’s party, rather than “painfully cool, underground-ish acts like LCD Soundsystem”. In fact, with her gif-worthy antics, ability to push the right pop cultural buttons, and the fact that she’s, erm, making art herself, Cyrus is totally in sync with Art Basel’s mood, and the party – jointly hosted by V magazine and Tommy Hilfiger – is the hottest ticket in town, with tempers boiling outside in a chaotic queue.

Inside, all is Gatsbyesque art deco splendour, with a stage set up at the far end of the hotel’s grounds, beyond a pool around which naked female performance artists are stalking, wearing only boots, wigs and a layer of body paint. While most events in Miami seem to start late, Cyrus hits the stage on the dot of 11pm with her friends the Flaming Lips, efficiently ripping through Rick James’s Superfreak. She’s wearing a silver glittery wig and what is essentially a mankini (albeit over silver tights), but it’s her charisma and vocal chops that impress. She really can sing, and also sell a song hard – during her 45-minute performance she effortlessly affirms that she’s a star. More problematic, in the parlance of 2014, is the appearance of a large black woman with her breasts out who seems to be there for little more than set dressing, providing more ammunition for those who accuse Cyrus of cultural appropriation.

Having evidently calculated that the crowd would prefer covers of rock classics than her own songs, Cyrus launches into the Turtles’ Happy Together. Backed by a synapse-frazzling light show, and given that it’s one of the most uplifting songs ever written, it’s a shrewd choice. There follows a long spoken ramble about how the previous year, despite the fact that it had catapulted Cyrus to superstardom after the twerking incident, had been the worst of her life, capped by the death of her dog – though this had led her to her current sideline as a sculptor. Despite the fact that Deitch compared Cyrus’s artwork to that of the late Mike Kelley, it’s safe to say that the artworld crowd greet this diatribe with some scepticism.

After a tortured piano ballad, Cyrus resumes what is essentially an upscale version of rock karaoke with a sweary version of Johnny Cash’s A Boy Named Sue and Led Zeppelin’s Since I’ve Been Loving You, navigating the song’s vocal gymnastics with a glorious ease. She’s then joined on stage by Wayne Coyne, whose association with her has been the subject of some disquiet among Flaming Lips fans. Though Justin Timberlake famously donned a dolphin outfit to perform with them on Top of the Pops, the band’s trajectory from America’s pre-eminent cult weirdos to Miley Cyrus’s backing band could surely not have been foreseen even by the wiry, wild-haired frontman.

That said, Coyne and Cyrus, now wedged into a giant rainbow, almost justify this strangest of career moves with two Beatles covers – Lucy in the Sky With Diamonds and A Day in the Life. As the Flaming Lips’ glitter canons and bubble machines roar into life, and men dressed as a mushroom and giant penis mill around the stage, it’s hard not to grin – though this turns into a worried frown when the topless woman reappears and Coyne buries his face in her cleavage.

Ultimately though, Cyrus put on an unpredictable, garish pop show with an edge of decadence (and not just because she smokes weed onstage), underpinned by undeniable talent, perfectly designed for an audience some distance from her normal fans. While the jury may be out on her art, there’s no doubt about Cyrus’s abilities as a performer – or of her ability to conjure a pop moment in the strangest of circumstances.