"Vasily Petrenko, 33." That's what it should say on the programme under principal conductor; all the players in the National Youth Orchestra have their ages listed, and Petrenko, their chief since December, cuts such a boyish figure he could almost be one of them. But once he is on the podium, there is no denying his authority.

Packed and buzzing as ever, the NYO Prom began with Tchaikovsky's First Piano Concerto, for which the orchestra's forces were trimmed to those of a normal-sized ensemble; for the second half, they were back to full, massive strength. But in every piece, Petrenko got them to play in the barest whisper, with absolute precision – something several professional ensembles find elusive.

The piano concerto brought Stephen Hough to the crest of his Tchaikovsky series, and once again demonstrated his ability to strip the Romantic Russian repertoire of its sentimental gloop without sacrificing its thunder. In the most fevered moments, Hough erupted, mixing unrestrained passion with purposefulness; yet it was in the quietest exchanges with the orchestra that he drew us in most irresistibly. The encore – his own, hushed solo arrangement of Tchaikovsky's None But the Lonely Heart – was a gem.

The second half offered two massive orchestral showpieces. In Lutoslawski's Concerto for Orchestra, the spirit of the pounding timpani at the start underpinned the whole of a performance that captured the work's menacing exuberance. Respighi's Roman Festivals brought an arresting opening from brass and percussion. If the end of the hazy harvest-festival episode slightly lost focus, the whirling fairground music of the final movement was spot on.

In both works, Petrenko looked like a conductor entirely confident of his players and able to enjoy himself with them. Snapping him up on his weeks off from the Royal Liverpool Philharmonic could be one of the best moves this organisation has made.