Murray, 21, returned to the court 26 hours after a downpour from Tropical Storm Hanna had left him leading two sets to love but a break down in the third to complete a 6-2 7-6 (7/5) 4-6 6-4 victory over Nadal after three hours and 30 minutes of play across the two days.
Murray now faces four-time defending champion and tournament second seed Roger Federer in tonight’s final, when the Scot will be the first Briton to contest a grand slam final since Greg Rusedski lost to Patrick Rafter in the 1997 US Open final.
Sixth seed Murray will be bidding to go one better than Rusedski and become the first British man to win a grand slam since Fred Perry succeeded at the US Open in 1936.
And despite having a day’s less rest than Federer, who knocked out third seed Novak Djokovic, Murray’s confidence will be sky high after a performance that displayed his new-found athleticism and mental strength as well as his natural talent.
Murray had been looking to get straight back in the groove against Nadal having taken that big lead on Saturday.
Both men were playing in their first US Open semi-final and play resumed on the main show court, Arthur Ashe Stadium, with Murray 3-2 down in the third as the sunshine returned to New York following a solid 12 hours of rain and the temperatures returned to the mid-80 degrees Fahrenheit.
History was still on 22-year-old Nadal’s side having won all five of his previous meetings with Murray, whose opening-set victory on Saturday had been the first time he had taken a set off the Spaniard since their first encounter at the 2007 Australian Open.
Nadal, the French Open, Wimbledon and Olympic champion, had admitted he was feeling tired and below his best coming into the US Open and had looked extremely flat in the gloomy atmosphere.
Murray said afterwards: “It’s awesome to beat him, a great feeling. He’s beaten me five times in a row, so that was tough, and to do it in a semi meant it was really difficult.
“With the rain delay, and it was windy today, there were a lot of different things, but I’m happy I came through in the end.
“It was really tough to serve from the near end, it was very windy, so I knew I was going to have chances to break and I just had to hang in,” he added.
Addressing his chances against Federer, Murray said: “It’s going to be tough.
“He’s played better the last couple of matches and played really well against Novak.
“He’s won here the last five times so to beat him in a final is tough, he’s got an unbelievable record.
“I’m going to have to play great if I want to have a chance of winning.”