By then, he had already won major national attention by winning, at the age of 13, the first prize for violin in the White Nights Festival in Leningrad in 1958. In 1969, he emerged on the international stage with a first prize in the International Competition for Violinists in Montreal, and the next year he was the second prize winner at the Tchaikovsky Competition in Moscow. At that point he went on the concert tour circuit throughout the U.S.S.R. and Eastern Europe.
He began appearing outside the Soviet bloc, debuting in the United States in 1975 with the New York Philharmonic, and gave a triumphant pair of recitals at Carnegie Hall in New York in 1976. In 1977, he toured as a soloist with the Moscow State Orchestra and debuted with the London Philharmonic. He was a particular favorite in America and in the next few years appeared with the Cleveland, Dallas, Pittsburgh, and San Francisco orchestras. Meanwhile he was studying conducting. He made his debut in that capacity at the very top rank of orchestras, leading the Chicago Symphony in 1979 at a Ravinia Festival summer concert. The press notices of that appearance make it clear that the occasion was a triumph, and it resulted in immediate engagements with other major symphonies around the world. Also in 1979, he founded the Moscow Virtuosi, which rapidly became known as one of the finest chamber orchestras of the world and celebrated its 30th anniversary with a special concert in London in 2009. He maintained both his solo violin career and his conducting. He conducted such groups as the Santa Cecilia Orchestra of Rome, the Leningrad (St. Petersburg) Philharmonic, the Houston Symphony, the London Symphony, and many international chamber orchestras, such as the English, the Scottish, and major chamber groups in Rome, Dresden, and the Netherlands. In 1989, he became artistic director of the Colmar International Festival in France. In 1998 he was appointed to succeeded founder Mikhail Pletnev as the principal conductor and music director of the Russian National Orchestra, the first privately owned orchestra in Russia since the 1917 Revolution.
He teaches at the Madrid Conservatory. He has been honored with Russia's highest prize, the National Cultural Heritage Award, and is Ambassador of the Arts of the World Economic Forum in Davos, Switzerland. He has established a Vladimir Spivakov Foundation to give creative and financial support for talented young people from around the world, and to needy children of Russia. He has also worked to raise relief for victims of Stalinism and children suffering from the Chernobyl power plant disaster. He is the founder of the European Sakharov Foundation.
He has recorded extensively for RCA Victor and conducts the Russian National Orchestra on the Well-Tempered Productions label. He played a violin bequeathed to him by his teacher Yankelevich, a 1716 instrument made by the Venetian luthier Francesco Bogetti, until 1997 when he was loaned a Stradivarius for life.