Palevsky was born on July 24, 1924 to Polish immigrant parents in Chicago, Illinois. He entered the U.S. Army after high school and after serving as a meteorologist in the Philippines during World War II, he attended the University of Chicago on the G.I. Bill, earning a Bachelor of Philosophy degree and a Bachelor of Science degree in mathematics and continuing on to graduate work in math and philosophy at the University of Chicago, the University of California, Berkeley, and the University of California, Los Angeles, where he taught Philosophy.
After working as a computer logic designer at Bendix Corporation and as the director of Packard Bell Computer Corp., in 1961 Palevsky founded Scientific Data Systems, Inc. The Xerox Corporation acquired the company in 1969, at which time he became a director and Chairman of the executive committee of Xerox Corporation. He retired in May of 1972. He was a founder and director of Intel Corporation in Santa Clara and went on to serve as a director of the American Civil Liberties Union, the Constitutional Rights Foundation, and People for the American Way. He also became a director and board chairman of Rolling Stone magazine, rescuing the publication in 1970 by buying a substantial share of the stock.
Palevsky produced several films, including Marjoe, which won an Academy Award for best documentary feature in 1973, Costa Gavras's State of Siege, Marcel Ophuls' Sense of Loss, Islands in the Stream and Fun With Dick and Jane. He also financed such films as Terrence Malick’s Badlands.
Since he moved to Los Angeles in 1950, Palevsky has been generous to the city's arts and culture. He rescued the Aero Theater (now run by the American Cinematheque) and bequeathed his collection of Arts and Crafts furniture and Japanese prints to the Los Angeles County Museum of Art. In lieu of flowers, donations should be be made to his favorite organizations: the ACLU, LACMA and the American Cinematheque.