Born in Chicago on 11 February 1919, Baker was the youngest of four children of Russian immigrants, and made his debut as a violinist in Chicago, aged six.
Later, he was concertmaster of Stokowski's All-American Youth Orchestra and a member of Toscanini's NBC Symphony Orchestra. After serving with the air force in World War II, he became a session musician and worked as concertmaster of Paramount Pictures' studio orchestra, playing for composers such as John Barry, Bernard Herrmann, André Previn, Franz Waxman and John Williams.
He also continued to work in the concert hall, working with Glenn Gould, Jascha Heifetz, Yaltah Menuhin, Gregor Piatigorsky and Igor Stravinsky.
Baker died on 25 December 2011, aged ninety two, at home in Studio City, Los Angeles.