Resuming his career after the Great War, Spivakovsky arranged to perform a monumental series of concerts with Maestro Wilhelm Furtwängler and the Berlin Philharmonic Orchestra, tracing the development of the concerto by all major composers from Bach to Brahms. This tour de force was a stellar success and he was hailed as a master of all musical styles, an exceptional exponent of the Three Bs, and the finest living interpreter of Brahms. The Leipziger Zeitung: "With his verve he reminds one of Anton Rubinstein, and with his precise and meaningful interpretation, of Bülow [Liszt's great student]." The Hamburgischer Correspondent: "The strongest piano talent I have encountered in the course of the last decade." And the Breslauer Morgen-Zeitung: "Who will explain this wonder-genius?"

He formed incomparable combinations with other legendary conductors, including Maestro Hans Knappertsbusch for the Tchaikovsky Piano Concerto in B Flat and Maestro Richard Strauss for his own Burleske. After a 1927 performance of the Tchaikovsky with Knappertsbusch and the Munich State Opera Orchestra, the Munchener Zeitung reported: "The solo part was played by the Russian, Jascha Spivakovsky, with a technical and musical finish such as I have never before encountered in this concerto. Our German pianists play such things too tamely in a Western fashion; but this Russian has the courage for the most extreme, he has the most fiery tempi, the most vigorous accents, the most tender and burning colours at his touch, the wildest limitlessness of crescendi, and yet always remaining – and this is the wonderful part if it – artistically restrained and fine." After a performance of the Burleske with Strauss and the Vienna Philharmonic Orchestra the same year, the Neues Wiener Journal reported: "Jascha Spivakovsky played the piano part in the Burleske unusually beautifully and full of life. Until now the piano music in this burlesque has been performed rather robustly, in a fortissimo-frenzy. The young Russian Spivakovsky, however, let the elegance, transparent beauty and clever wit of the piano-voice emerge. With economy of fortissimo and such fineness in the run-playing and figurework, the architectural beauty of this piece was discovered for the first time."

Throughout the Golden Twenties, Spivakovsky sparked scenes of wild enthusiasm reminiscent of Lisztomania in the 1800s. His 1921 season was "the sensation of London" and a crowd of 3000 clamoured outside his sold-out final concert at the Albert Hall. The London Daily Chronicle reported: "It is a long time since we have heard such playing, technically faultless, and with such overwhelming passion." At his Australian debut in 1922, the entire audience rushed the stage, clamoured for favourites until the piano was taken away, then rushed backstage until the lights were turned out, then beseiged his motor car which was quickly overrun by young ladies. The Head of Pianoforte at the New South Wales Conservatorium declared in a newspaper report: "I have never witnessed such a scene in Australia" and other commentators referred to an outbreak of Spivomania. After a recital in Spain in 1927, El Castellano reported: "the enthusiasm of the public actually took them to the very doors of the Coliseum as a sincere tribute of farewell to the artist who had been able so well to win them over and overcome them." After a recital in Italy the same year, the audience followed Spivakovsky en masse through the pouring rain to his hotel, where they continued to applaud until he took a final curtain call from the balcony.

Unlike many of his contemporaries who became known for specific composers or periods, Spivakovsky was equally at home with all musical styles and had a vast repertoire. From the Brisbane Courier in 1922: "A rare faculty which enables him to pass from one stupendous composition to another, or from lightest shades to darkest gloom, investing each with the composer's individuality, and at the same time preserving his own strong personality." The Wiener Allgemeine Zeitung in 1927: "A pianist whose technique commands the Liszt school as well as the modern. A dreamer and a stormer at the same time." and The Register in 1929: "He seems to call up the spirit of each composer in turn."

He championed many modern works, including Max Reger's titanic Variations and Double Fugue on a Theme of Bach and Modest Moussorgsky's Pictures at an Exhibition. After he gave Australian premieres of these works in 1929, the Sydney Sun reported: "the audience realised that a genius of the piano had come to them" and the Sydney Mail noted his "remarkable emotional range and interpretive powers of the highest degree." He also pioneered radio broadcasting in Australia, giving the first live concert wireless broadcast to the Australian public on 31 March 1922. The Argus reported: "Spivakovsky has electrified Sydney audiences, but he was thrilled himself today by the knowledge that he was flashing his music a distance of 500 miles in one-fifteenth of one second … he said that playing to unseen audiences hundreds of miles away had proved the most thrilling time he had ever spent at the piano."

Always a lover of chamber music, he also founded a duo in 1920 with his younger brother Tossy, a thirteen year old violin prodigy who had debuted in Berlin with huge success three years earlier. The brothers had toured together as soloists and become major celebrities in Denmark after performing for the royal family. They performed as The Spivakovsky Duo throughout the Twenties and recorded for Parlophone, becoming famous across Europe for artistic virtuosity, warm expression and perfect unison. Among their biggest fans was the amateur violinist Albert Einstein. Tossy was soon recognised as one of the finest violinists in the world, pronounced "the young Joachim" by leading critics and appointed the youngest-ever concertmaster of the Berlin Philharmonic Orchestra by Maestro Furtwängler.