Rafael Nadal, the French Open and Wimbledon champion, has not lost to the Scot in five previous meetings but, like his opponent, was competing in his first US Open semi-final.
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Murray, a winner of three ATP titles this season, broke Nadal in the third game of the match when the Spaniard hit a forehand long and again in the seventh with a forehand pass down the line to lead 5-2 and went on to clinch the set.
It was the first time the Scot had won a set against Nadal since their first encounter at the 2007 Australian Open.
Nadal had to work hard to hold serve in the second, saving two breakpoints in the fifth and 11th games before the set went into a tiebreak.