The British former world number one played in a manner reminiscent of his best as he led by two sets to one. But Tsitsipas fought back to win 2-6, 7-6 (9-7), 3-6, 6-3, 6-4 in New York.
Dan Evans is the only Briton through after defeats for Heather Watson, Harriet Dart and Cameron Norrie.
Murray, like so often in the past, was the British player who stole most of the attention on the opening day of the final Grand Slam of the 2021 season – even in defeat.
Fired up throughout and relishing the magnitude of the occasion, 34-year-old Murray moved freely and hurt Tsitsipas with his quality from all over the court.
A seismic shock beckoned before 23-year-old Tsitsipas – one of the favourites for the title – maintained his focus and bided his time to win in four hours 49 minutes. (BBC)