Spivakovsky resumed international touring after the chaos of World War II, returning to Great Britain, Europe and Australasia and broadening his reach to the United States, Canada, Israel, India, Singapore and North and South Africa. His relentless touring schedule followed the winter concert season around the world non-stop for the next twelve years, making up time for the previous twelve years when he had put his career on hold due to world events.

After the chaos of World War II, Spivakovsky resumed touring Great Britain, Europe and Australasia and expanded his reach to the United States, Canada, Israel, India, Singapore and North and South Africa. During his first post-war world tour in 1947, the legendary British critic Sir Neville Cardus printed: "It has been a rare experience. I knew Jascha Spivakovsky was a splendid pianist, of course; but I didn't know he could so take the measure of some of the greatest works in piano literature." John Sinclair, one of the leading Australian critics (and one of the leading reasons William Kapell vowed never to return to Australia) printed: "From whatever angle one viewed the performance it was stamped with unmistakeable signs of rarity and greatness … I have the choice between futile and inadequate language and silence."

He also championed new works by composers such as Bloch, Kabalevsky and Saeverud and continued to perform earlier modern works by composers such as Reger, Katchaturian and Prokofieff. Unlike many of his contemporaries, he was able to render the modern percussive style without losing the expressive qualities of the music. From Bergens Tidende after a performance of Bloch's monumental Concerto Symphonique under the direction of Hugo Kramm: "a supreme pianoforte player, with phenomenal force and a warm temperament. It was difficult to imagine that this piano work could be rendered in a more perfect manner."

After Spivakovsky retired from touring for health reasons in 1960, he performed only rarely for charity and celebrity concerts. By this stage he had been broadcast on radio and television stations around the world and performed with virtually every great conductor of his era, including Arthur Nikisch, Leo Blech, Issay Dobrowen, Willem Mengelberg, Felix Weingartner, George Schneevoigt, Wilhelm Furtwängler, Hans Knappertsbusch, Richard Strauss, Sir Henry Wood, Sir Thomas Beecham, Efrem Kurtz, Sir Adrian Boult, Sir Malcolm Sargent, George Szell, Maurice de Abravanel, Sir Eugene Goossens, Josef Krips, Pierre Monteux, Paul Kletzki and Leonard Bernstein.

He continued to teach extensively and mentor younger pianists including William Kapell, Julius Katchen and Shura Cherkassky. He also continued to lead the Australian Friends of the Israel Philharmonic Orchestra, which he had founded in the late Thirties at the request of his friend and colleague Bronislaw Huberman. He raised funds for the orchestra's first visit to Australia in 1966 and encouraged them to engage the young, outstanding conductor Zubin Mehta for the tour. A cultural beacon for eminent artists visiting Australia in the interwar and post-war periods, he welcomed many friends and colleagues to his much-loved adopted home over the years, including Pavlova, Melba, Huberman, Galli-Curzi, Fischer, Elman, Schnabel, Szell, Artur Rubinstein, Arrau, Moiseiwitsch, Friedman, Kapell, Bernstein and Borge.

One Spivakovsky hallmark inherited from Anton Rubinstein was extraordinary tonal command, which critics noted from his earliest performances but focused on increasingly post-war. After a performance at Carnegie Hall in 1948, the Brooklyn Eagle reported: "Virtuosos are plenty, tonalists are comparatively few. Happily we have one here. If fireworks are called for Mr Spivakovsky very obviously can provide them. What is more, in doing so he is able not only to play the notes but to play the music as well." After this concert Vladimir Horowitz went backstage to congratulate Spivakovsky and told him: "Back in Russia when I was four years old, my mother dragged me through snowdrifts twenty feet deep to hear an outstanding prodigy. YOU were that prodigy." The same year the Manchester Guardian reported: "How truly depth of feeling combined with strength and beauty and subtlety of expression … the range of tone was immense, and the pianist's power and variety of touch were put to noble use."

Another Spivakovsky hallmark entirely his own was exceptional clarity of texture, which critics also noted from his earliest performances but often had trouble putting into words. As the New Zealand Times commented in 1922: "He has to be heard before he can be understood. Mere wealth of verbiage gives little real idea of the man as the artist, the genius, the virtuoso." Eventually in 1953 Sir Neville Cardus coined the descriptor "crystal piano-playing" after hearing Spivakovsky perform Mozart's Piano Concerto in A major with "extraordinary purity and clearness." His wife Lady Edith Cardus had telegrammed Spivakovsky after hearing him perform the same concerto a few years earlier: "The best Mozart playing have ever heard."

In his tome The Piano in Concert, the renowned Hungarian-American critic Professor George Kehler also attempted to translate Spivakovsky's unique "crystal piano" sound signature into words: "Characterised by the attributes of the Russian School – a remarkably rich and full tone quality (which cannot be adequately described) together with a very strong, consistent rhythmic impulse and an almost incredible legato. The legato enabled him to highlight the melodic line without pedalling, giving great unity to the overall concept without losing the fine detail. The sparing use of sustaining pedal gave great clarity of texture, which critics referred to as 'crystal piano-playing', an effective blending of the best of the old and new schools. Other critics who witnessed Spivakovsky's performances thought him to be an extraordinary artist, a musician of the masterly order, of great physical and intellectual power, an unsurpassable performer."