The South African won 7-6 (7-5) 6-3 6-7 (2-7) 7-6 (7-0) in four hours and 18 minutes to reach a first major quarter-final.
It is the first time since the 2010 US Open that Murray has lost before the quarter-finals of a Grand Slam.
Britain’s two remaining singles hopes faded within 12 minutes of each other as Jo Konta of Britain also lost 7-5, 6-3 to Petra Kvitova in the women’s singles.
While Konta’s 16-match winning run ended in straight sets, Murray’s hopes disappeared in a fever-pitch atmosphere on Louis Armstrong Stadium.
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It’s been 38 years since Britain had male and female quarter-finalists at the same Grand Slam, but Murray’s defeat means it is the first time in five years there have been neither.
Murray who has had a run of 18 Grand Slams in which he made at least the quarter-finals, expressed his disappointment on losing this one.
Murray said, “That’s obviously something that is disappointing to lose,”
“Obviously that’s many years’ work that’s gone into building that sort of consistency. To lose that is tough.”
Meanwhile, South Africans Kevin Anderson will play Stan Wawrinka in the quarterfinals.