After 11 years under chief conductor Sakari Oramo, the BBC Symphony Orchestra is used to having a Finn on the podium. Here, though, it was the Proms debut of the latest conducting phenomenon to come out of Helsinki. Tarmo Peltokoski has studied with everyone who is anyone in Finnish musical circles, from Oramo himself to Esa-Pekka Salonen. A series of high-profile appointments, which inevitably make much of his age – he’s 24 – have generated a buzz. There’s substance too, as evidenced by his airy account of Vaughan Williams’ Fantasia on Greensleeves which opened the programme.

A lurching gear change saw Patricia Kopatchinskaja go head-to-head with Schoenberg’s Violin Concerto, a work she introduced as “unplayable”, unless of course the violinist is endowed with an extra finger (for the record, she isn’t). Nevertheless, she took the plunge, playing with elfin grace and demonic fury in equal measure, her body shimmying with sheer delight in a work she clearly adores.

Kopatchinskaja managed to convey both the music’s inner logic and elusive spirit, guiding the listener along even the thorniest of paths. Playing with exceptional sweetness, especially in the upper register, and relishing each of Schoenberg’s motivic sidesteps, she unearthed several waltzes, a tango and a militaristic march along the way as she skittered and swerved through one of the toughest nuts in the repertoire. Peltokoski was a thoughtful partner, clarifying some knotty textures, before joining Kopatchinskaja in a pair of hilarious encores, the second requiring him to quack like a duck (you needed to have been there).

His Shostakovich – the Fifth Symphony – was more of a mixed bag. The long first movement was full of interesting ideas that somehow never quite cohered. Inclined to podium theatrics, at times Peltokoski simply didn’t get from the orchestra what his flamboyant gestures seemed to demand. All was forgiven in the Largo, however, a hushed, exquisitely textured and deeply moving essay in which conductor and orchestra roamed a frozen wasteland of silent desperation. In 15 heart-stopping minutes, Peltokoski showed what all the fuss was about, before clearing the air with a textbook finale that fizzed and roared in all the right places.

• Available to listen again on BBC Sounds until 13 October. The BBC Proms continue until 14 September.