Istomin was born in New York City of Russian-Jewish parents. He was famous for his work in the piano trio, with Isaac Stern and Leonard Rose, known as the Istomin-Stern-Rose Trio, with whom he made many recordings, and particularly of music by Beethoven, Brahms and Schubert. He also played with them in orchestral music, with conductors such as Eugene Ormandy, Bruno Walter and also as a soloist.
In 1943 he won the Leventritt award, and also the Philhadelphia Youth Award. He made his debuts with the Philadelphia Orchestra with Eugene Ormandy, playing a concerto by Chopin, and the New York Philharmonic conducted by Artur Rodziński playing Brahms' Piano Concerto No. 2 in the same week in 1943.
He won a Grammy Award in 1970 with the trio, for their recordings of Beethoven.
He recorded extensively for Columbia (later Sony Classical) solo works and chamber music.
He married Marta Montañez Martinez (Marta Casals Istomin), the widow of Pablo Casals, on February 15, 1975. She is a former president of the Manhattan School of Music and former artistic director of the Kennedy Center for the Performing Arts in Washington, D.C. He moved to Washington in 1980.
In the 1980s and 1990s he gave recital tours in which he toured 30 American cities with his own pianos and piano tuner.
He received the French Legion d'Honneur in 2001.
He died of liver cancer in 2003 at his home in Washington.