In the year since her debut album The Fame was released, Lady Gaga, aka 23-year-old Stefani Germanotta, has sold more than 10m records and made the kind of impression that reminds one of the emergence of another ambitious bottle-blonde from New York, Madonna. Now she is hoping to take it to the next level with her version of Madonna’s spectacular globe-spanning mega-tours.

Germanotta describes her Monster’s Ball tour as the “first ever electro-opera” and “the greatest post-apocalyptic house party that you’ve ever been to”. I left the O2 Arena no wiser as to what an “electro-opera” or “post-apocalyptic house party” might be. But I also left with ringing ears, dazed retinas and a sense of awe at the crazed invention of the Gaga wardrobe. Contrary to her ladyship’s imaginings, I doubt even the most rabid fans, the ones tricked up in Gaga make-up and outfits, thought they had witnessed a “Rites of Spring”-style musical landmark – but it certainly bore all the hallmarks of the best arena entertainment.

The story, a back-of-the-envelope cross between The Wizard of Oz and The Rocky Horror Picture Show, told of Gaga and friends’ attempts to go to the demi-mondaine Monster’s Ball, where “everyone can be who they want to be”. In reality, the plot was as flimsy as the costumes (the ultra-buff male and female dancers looked like they were modelling a 1980s underwear catalogue devised by Robert Mapplethorpe), but a knockout array of effects, beefed-up versions of The Fame’s tracks and Gaga’s singular stage presence guaranteed the evening’s success.

An admirer of Andy Warhol, Germanotta is an artificial, highly stylised performer. The show opened with her silhouetted behind a screen performing abbreviated movements to thunderous synth lines. Then the screen fell away to show her in a purple leotard with vast shoulder pads – imagine a camp American footballer throwing shapes at Studio 54 – and with lips painted in exaggerated red lipstick and thick, black silent movie-star eye-liner. “I hate the truth,” she later announced. The past decade has seen the irresistible rise of memoir: Lady Gaga is the backlash against it.

With a catwalk extending into the audience and a stage set that at various points included a car with a piano under its bonnet, a haunted forest, a New York subway train and a huge tentacle-waving monster, the controls were set to stun. “Just Dance” was a sensory overload of formation dancing, wild guitar solos, flashing lights and hallucinatory visuals. “Money Honey” opened with Lady Gaga playing grandiose prog rock chords on a specially devised “key-tar” in the manner of Rick Wakeman. The music was generally impressive, with stomping glam beats and reverberating basslines transforming The Fame’s tinny songs into arena-quaking synth-pop. The vocals were unshowy but powerful. The ballads, usually the signal for a mass exodus to the bar, hit home with power chords and gutsy singing, delivered by Gaga sitting at the piano in a tiny leather bikini, one thigh-high boot insouciantly resting on the keyboards.

Her trademark self-designed costumes did not disappoint. One section found her sporting a rectangular red outfit, like a cubist Cardinal. Another saw her sporting what looked like the pelt of an enormous Afghan hound. Gothic themes added darkness to the pantomime make-believe. There was a surprising emphasis on death, and several of the images projected on screens – Gaga eating a bloody heart or smoking a cigarette in a gimp mask – were downright unsettling. Madonna again came to mind: like many of the finest pop stars, Lady Gaga occupies a bold, self-invented place between the deviant and the mainstream