Alexander Uninsky was born in Kiev (then in the Russian Empire, now in Ukraine). He initially studied piano there in the conservatory which had been opened in 1913, and whose other graduates included Vladimir Horowitz and Alexander Brailowsky.
He subsequently moved to Paris in 1923, where he studied with Lazare Lévy. He was awarded the conservatory's first prize for piano. In 1932 he won the II International Chopin Piano Competition.[2] In fact, Uninsky tied for first place with the blind Hungarian pianist Imre Ungar, and the judges decided to award victory on the basis of the toss of a coin. Ungar lost.
In 1955, he took up a teaching post at the Toronto Conservatory of Music, where he numbered among his pupils the Canadian composer Bruce Mather. Mather commemorated his teacher in his 1974 composition In memoriam Alexander Uninsky
Subsequently, he taught at the Southern Methodist University in Dallas, Texas. His pupils included Jeffrey Swann, David Morgan, Carmen Alvarez, Boaz Heilman, Dr. Henry Doskey, David Golub and Dubravka Tomšič Srebotnjak.
He played his last concert in San Jose, Costa Rica, on October 19, 1972 for the celebration of the 75th anniversary of the National Theatre. He played Tchaikovsky's Piano Concerto #1 Opus 23 with the Costa Rican National Symphony Orchestra conducted by Gerald Brown. He was suffering an advanced arthritis.
He died in his sleep two months later, on December 19, 1972 in Dallas, Texas, aged 62.
Uninsky was quickly signed up in the early 1950s by the newly formed Philips recording company. His Chopin playing is well represented in his recordings, including the complete Études, recorded in the 1950s, the complete Mazurkas and Impromptus recorded between 1959 and 1971, the Scherzos and Waltzes, as well as the piano concertos. His other recordings included works by Liszt.