The British No.1 came through a four-hour battle with Argentina's Juan Martin Del Potro to win 7-6 (7-2), 7-6 (7-1), 4-6, 7-5.
Murray will now play in the last four of a grand slam for the first time on Saturday against the man who is the dominant force in world tennis.
Murray said: I’m excited to be in the semi-final, but the tournament is still going on.
When I watched the first night session of the tournament and saw all the winners of the US Open, I realised that winning is what really, really counts. I want to win.
I don’t care what happens throughout the course of a match as long as I win.
Nadal, who beat Murray in the Wimbledon quarter-finals this year, came through with a four-set victory over America's Mardy Fish 3-6, 6-1, 6-4, 6-2.
Needing to break 19-year-old Del Potro to avoid a third tie-break, Murray finally drew some errors from the racquet of his in-form opponent.
The 17th seed has rocketed up the rankings by winning his last four tournaments and was aiming to continue a 23-match winning streak.
I knew it was going to be a tough match, continued Murray. He’s won 20-something matches in a row. I didn’t think I was the definite favourite.
Before advancing, Murray had to overcome a third-set collapse after taking three of the first four games.
Leading 4-3, Murray had two break points but could not capitalise and he was then broken for the second time in the set as Del Potro reduced his arrears and increased his confidence.
Despite the lapse, which resulted in the Scot having to battle through a titanic fourth set, Murray was happy with his strategy.
I knew I was going to have to fight a lot and change the pace of the ball, because he’s really solid from the back of the court, he said. My tactics worked quite well.
Murray also lost a sizeable lead in the first set and wasted a chance to serve for the second set, but still managed to keep the upper hand.
I was in the driver’s seat, up two sets, Murray admitted.
There was a bizarre exchange during the first-set tie-break as Murray asked officials to turn off the large video screen located high above the seats at Arthur Ashe Stadium.
I just asked them if they could turn it off, and he (the umpire) said no,
Murray explained. I said, ’That’s absolutely fine.’
The altercation did not affect Murray, however, as he reeled off six consecutive points to clinch the set.