“A riddle, wrapped in a mystery, inside an enigma.” That description could apply to Shostakovich’s Fifteenth Symphony, with its impish musical quotations punctuating its dark brooding character. It would also describe Valery Gergiev’s conducting. The Mariinsky maestro relinquishes the LSO hot seat at the end of 2015. I’ve watched Gergiev more than any other conductor over the past two decades and even now I’m at a loss to explain his technique. The scowl, the hummingbird fingers, the toothpick baton… it shouldn’t work. Yet, in the right repertoire – invariably Russian – the results can be sensational.

Balakirev’s Islamey kicked off proceedings with a dash of oriental splendour. Never underestimate the value of a good concert opener; programmers neglect them at their peril. They help settle an audience – an orchestra too – but vitally, they quickly test the waters, providing a musical barometer for the evening ahead. Gergiev charged headlong into Lyapunov’s exotic orchestration, resulting in a few ragged entries and blurry ensemble. However, a few grunts from the Russian bear on the podium and everything snapped into focus; an orchestral explosion of colour concluding this dazzling curtain raiser. Pulse raised, job done.

Gergiev then took a back seat for Tchaikovsky’s Violin Concerto, which is not to say he set the LSO on cruise control. He subtly balanced accelerator and brake to provide a most attentive podium partner, the orchestral ebb and flow feeling almost improvisatory. After the orchestral tutti, Nikolaj Znaider immediately took control, brusquely grabbing the concerto by the scruff of the neck to give an immensely personal reading. Burnished lower notes gave way to nut-brown sweetness and lyrical intensity at the top. The first movement cadenza was a remarkable piece of storytelling, Znaider’s 1741 Guarneri playing both seductive Scheherazade and her gruff Sultan.

Even in the Barbican’s wide expanse, the Canzonetta achieved a chamber music intimacy, particularly in the exchange between violin and clarinet, before we stamped the snow from our boots for an exhilarating Cossack finale, fast and frenzied. A Bach Sarabande brought balm to the ears as an encore.

Shostakovich’s final symphony is like a giant canvas, sparsely painted, where the artist only reveals part of the picture at any one time. Rarely does the entire orchestra play together, but a mosaic, a patchwork of sound, is unveiled section by section. Gergiev, head buried in the score, toothpick directing the traffic, busied his way through the “toyshop at night” as the composer described the first movement. The childlike innocence of the perky flute theme, Gareth Davies on splendid form, soon gave way to a battery of percussion and the brass impudently quoting the galop from Rossini’s William Tell overture. Gergiev played it completely deadpan. Is Shostakovich playing games here? Is he thumbing his nose at authority?

The riot of percussion soon gave wave to the sombre brass of the second movement. Every bar seemed wrenched from the heart, the spotlit score throwing the focus on Rebecca Gilliver’s eloquent cello threnody, or the vibraphone, or a slippery double bass. Gergiev elided into the spiky scherzo, demonic solo violin and grotesque percussion to the fore, in a movement which quotes Shostakovich’s own musical signature “DSCH” (D, E flat, C, B natural).

Two Wagner quotes open the fourth movement; the "fate" motif from Gotterdämmerung and the opening notes from Tristan und Isolde which morphs into an insouciant waltz. Again, why these particular quotations? You get the sense that Shostakovich is teasing, toying with your brain. If Gergiev knew the answer to these riddles, he wasn’t letting on. Few conductors can charge Shostakovich with such electricity and I cannot imagine hearing this symphony played more superbly. In the eerie finale, against a frozen high chord on the strings, percussion clicked and whirred and chattered until the clockwork ground to a sinister halt. Gergiev even commanded the silence.