Hockney's 1972 work Portrait of an Artist (Pool with Two Figures) was described by Christie's in NY as "the holy grail of his paintings, from both the historical and the market perspectives" before it went under the hammer.
The price was driven up in a bidding war between two telephone bidders - overshooting its estimated value by £8m.
The previous record by a living artist was held by Jeff Koons, whose "Balloon Dog" sculpture sold for $58.4 million at Christies in 2013.
Alex Rotter, co-chairman of post-war and contemporary art at Christie's in NY, said the painting reflects both the European and the United States perspectives of Hockney who went to live in California in the 1960s and saw himself as living on both continents.
The painting, whose buyer was not immediately revealed, had been long held by a private collector.
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Portrait of an Artist (Pool with Two Figures) shows a man in a swimming pool and another man in a red blazer standing by the pool and looking down. The Times reported that, earlier this week, a Sotheby's auction produced new highs for three African-American artists and a 42-year-old female painter. Hockney's 1972 work depicts a landscape reminiscent of the South of France containing two men including the artist's former lover Peter Schlesinger.
Hockney first worked on a similar painting in 1971 after being inspired by two pictures juxtaposed on his studio's floor.