The 26-year-old Italian pianist Beatrice Rana made her concert debut aged nine with the Bach Keyboard Concerto in F minor BWV 1056, so it was no surprise she sounded right at home playing it with the Amsterdam Sinfonietta at the Concertgebouw on Saturday for the last of eight concerts in a mini-tour of soloist and ensemble made in heaven. I have no way of knowing what the learning curve may have been from the first concert, also in Amsterdam, on 30 March to the grand finale, but there was no question that on Saturday night soloist and ensemble were playing as one – and were accorded a standing ovation.

Whatever Rana did on the keyboard was echoed, when called for, precisely by the Sinfonietta's magnificent strings, and vice versa. And the ensemble faded gently into the background when Rana, playing on an open-topped piano with her back to the audience, let rip with one after another of the stunning cadenzas or trills that are embedded throughout the two Bach concertos on the menu that night – the F minor and its more famous companion, the D minor BWV 1052.

Rana, for those who have missed the growing buzz about her, is the daughter of pianist parents and began studying piano at age four. She won first prize at the Montreal International Piano Competition in 2011 and silver in the Van Cliburn competition in 2013. She also is under contract to Warner Classics and has released four well received CDs.

Whenever “young” and “Goldberg” appear in the same sentence they conjure up the spirit of Glenn Gould, but Rana does not seem to be treading that path. She does not sound as mystical, for one, and if Gould wrestled with squaring the circle of performing Bach on an instrument the composer never knew, Rana dives right in. Her runs and trills are forceful, when called for, and delicate and subtle when needed. In the poignant second movement of the F minor, which seems a kissing cousin to the Goldberg, she seemed to have distilled all the beauty of the entire set of variations into one gorgeous, soulful movement. The finale of BWV 1052 zoomed along, not at too rapid a pace, but an exhilarating one.

It made for a thrilling evening of Bach, but that was not all that was on the programme. The Sinfonietta and their leader, Candida Thompson, opened with Mozart's evergreen Eine kleine Nachtmusik, a piece embedded in the world's sonic background noise. The Sinfonietta's playing was polished and beautiful while Thompson's crystal clear lines in the third movement made an all too familiar work sound as fresh as the tulip-bedecked spring weekend enveloping the city outside.

Rounding out the programme was Bartók's Divertimento for Strings, composed in 1939, the year before the composer and his wife, Ditta Pásztory, moved to NewYork to escape the growing alignment of his native Hungary with the Nazi's Axis alliance. The first movement is a waltz studded with gypsy-style melodies and syncopated rhythms – perhaps a wistful glance backwards to the world Bartók knew he would be leaving behind. The second movement is marked Molto adagio and contains a series of ominous, ascending string slides that culminate almost in a shriek, before fading away again to nothing. A premonition by Bartók of what was to come in a Europe overrun by the Nazis and war? The Sinfonietta's performance made your hair stand on end – so consider the job done.

Ominous Bartók, polished Mozart and energetic Bach, all on a superb musical spring evening in Amsterdam.