A velvet-smooth bass-baritone voice, matinee idol looks and magnetic stage presence have made Erwin Schrott into one of opera’s big international stars. Last night, however, festivalgoers at Budapest’s Comedy Theatre saw him excel in a very different musical form: the Argentinian tango music whose leading composer was Astor Piazzolla. Since winning prizes with his 2011 album Rojotango, Schrott has been playing the music of Piazzolla and others with his Rojotango Ensemble.

The concert opens with the musicians filing onto a darkened stage. In a half light, we hear eerie, broken sounds from piano, guitar, double bass, bandoneon; as the lights are raised, these coalesce with the rest of the nine piece ensemble into a driving, pulsing rhythm. Schrott is in the middle with his back to us; as the lights come fully on and the rhythm reaches its full intensity in the familiar 3/3/2 of the tango, he turns to us, lifts the microphone and starts an almost rap-like vocal, morphing into full voice for the main melody. I don’t know which the opening number was – the programme showed most of the works played but not the running order – but it left us breathless.

Schrott’s voice is the sound of luxury – smooth, deep, rich, melting. If it were a foodstuff, we decided, it would be Valrhona chocolate. He uses several voices in the course of the evening and switches seamlessly between them, from the rapid fire stuff of his opening to a whisper, a spoken or half-sung style or the full-on chest voice. Surprisingly, for an opera singer, his microphone technique is impeccable.

The next number, Piazzolla’s Milonga del Angel, brims with nostalgia. Piazzolla was an aspiring classical composer before he ended up fusing the tango styles of the bordellos of Buenos Aires with jazz and his classical training into his own unique style, which is sufficiently unlike anything else that if you’ve never heard any before, I’m not going to succeed in giving you the full flavour. But here’s one key thing: Piazzolla is a master at portraying wistful nostalgia in a way that somehow lifts the heart. He described himself as loving listening to Schumann and Mahler because it made him sad - “Music is a sad thing, but I feel happy in the company of sadness”.

Next is Oblivion, not a tango, but a slow song that overflows with thoughts of what might have been. Piazzolla’s original is instrumental, but Schrott performs it with French words by Julien Clerc, ending in the repeated “J’oublie” (I forget). It’s a tune which never fails to bring tears to my eyes. I was in floods by the end, yet uplifted.

The ensemble is jam packed with virtuosi, and, jazz-style, most of them get their chance to shine. Guitarist Alvaro Rovira plays several extraordinary solo introductions that would happily grace a classical recital in a sort of flamenco-infected version of Barrios or Villa-Lobos. Pianist Federico Lechner plays a jazzy solo intro that is so fine that Schrott stops him for the audience to applaud and then tells him to do another different one: he and bassist Gina Schwarz oblige with something equally amazing. A key instrument in any tango ensemble is the bandoneon, a South American variant of the concertina: Claudio Constantini is impressive throughout and, in one of the encores, pulls off the extraordinary feat of simultaneously playing piano with his left hand and bandoneon with his right.

On drums, Ingrid Oberkanis spends much of the evening demonstrating a rare ability to play softly and provide rhythmic base and drive without becoming too loud for the other musicians, sometimes playing with palm of hands and a stick at the same time. Her chance to shine comes in the instrumental Libertango: after the steady build-up of a mesmeric repeated phrase, Oberkanis powers the ensemble as it bursts into life for the main theme.

One of the magical components of this music is the holding of a long, slow, lyrical violin or vocal line over the rapid, insistent tango rhythm, often punctuated by stabbing chords on the bandoneon. Schrott’s operatic credentials are well in evidence as he delivers these long phrases with lilt and perfect control. Schrott is also good at working the crowd, whether joking with the slightly terrified-looking Hungarian woman whom he has beckoned on stage to help him translate, getting us to sing the refrain of Caetano Veloso’s Desde que o Samba é Samba – in Portuguese for those who could, “la la la”s for those who couldn’t – or reminding us that this is a charity concert to support World Awareness of Autism Day.

Piazzolla died in 1992; one of the members of his last band was Pablo Ziegler, who wrote the song Rojotango after which this ensemble is named: Schrott relates with a flush of pride and a lump in the throat the tale of how he met Ziegler in his Brooklyn apartment and Ziegler gave him the music. It’s a real barnstormer and Schrott throws everything into it, providing an exciting close to the programme (and again, reprised, to close the encores). It sent us away into the cool spring air with a thrill.