The world number four felt the hard courts of Flushing Meadows gave him a better chance than he had had at the French Open or Wimbledon but in the first two sets Nadal was simply too good.
Murray, who beat the Spaniard at the same stage here three years ago, fought back valiantly but he let the momentum slip away at the start of the fourth set and it proved crucial.
Nadal will play Novak Djokovic in the final on Monday in a repeat of the Wimbledon showpiece, which was won by the Serbian.
The Scot enjoys playing Nadal and he seemed calm and confident at the start as he withstood a barrage in his first two service games, coming from 0-30 down both times and saving a break point in the second.
At 3-2 Murray had his chance to break but he drilled a backhand wide and Nadal eventually held with the sort of running forehand down the line he has made his trademark.
The next game the fourth seed did come unstuck. He screamed in annoyance as he was beaten by a Nadal lob on the first point and, although he saved two break points, a mishit on the third gave his opponent the game.
There had been doubts about the champion’s form heading into the tournament but he was playing brilliantly and clinched the first set in 55 minutes when Murray netted a forehand.
Like the opening set, Murray came through a tricky game at the start of the second, and then came his big chance.
Three times the Scot brought up break point on the Nadal serve but he could not take any of them, dumping backhands into the net on the two where his opponent missed his first serve.
Not taking chances against the world number two usually proves costly and that was the case again in the fifth game as, after saving one break point with a great volley, Murray steered another volley wide to put Nadal 3-2 ahead.
The Spaniard then made it four games in a row when another stunning forehand winner set up a fourth break point.
However, as in their Wimbledon semi-final clash last year, Nadal lost his concentration slightly at the start of the third set and Murray pounced, at last taking a break point.
Two disappeared but on the third the fourth seed played with power and patience, testing Nadal again and again on his backhand before finally putting away a volley.
Murray gave back the break straightaway with a double fault and a netted backhand, while another break point disappeared in the fourth game.
But, unlike Wimbledon, he got another chance and grasped it, forcing Nadal into a backhand error.
Serving out the set was not altogether straightforward, the 24-year-old seeing two set points slip away, but he created a third with a brave volley and this time Nadal netted his return.
Only Roger Federer has come back from two sets down to beat Nadal, and that was when the 25-year-old was a teenager – but the fact Murray has won matches from such a position six times in his career, including in the second round here against Robin Haase, gave him a sliver of hope.
The start of the fourth set was key and in the third game he fought back from 40-0, including winning a point with a broken string, to force a break chance, but he netted a backhand and again it returned to haunt him.
Murray saved two break points in the next game but could not wrap it up and he will feel he rather donated the break in the end with a double fault and a missed forehand.
It was the boost Nadal needed and, although Murray courageously staved off three break points in the sixth game, it was not enough as the second seed clinched victory in three hours and 24 minutes.
He told Sky Sports One: “I’m disappointed with the way I played in the first two sets. The third and fourth were better but it wasn’t good enough.
“I don’t know if I didn’t want to play too many long rallies because I had a long game yesterday but it’s the only way to win against him. Playing one-two tennis against him doesn’t work because he makes too many balls.
“There are many things I could have done a bit better tonight – but I didn’t.
“He’s probably the greatest player to play tennis so it’s easy from the sidelines to say how you should play against him.
“I’ve played many different styles against him and the most success I’ve had is solid from the baseline, giving it a lot of height up to his backhand.”
The Scot added: “I’ve just got to improve because it’s very disappointing to get close.
“I’ve lost to him this year a few times in big matches. I just need to keep working on my game and getting physically stronger, that will help.”
Nadal said afterwards: “I think I have played my best match this year here, so I’m really happy to be in the final.”
However, he acknowledged Djokovic is likely to present a formidable barrier, explaining: “This year I’m not having a lot of luck against him – I’ve played five finals and lost all of them.
“I haven’t found a solution yet but I’ll try my best. I’ll have to be very solid with my serve. New York, help me this time!”
Nadal acknowledged the significance of the final taking place on the 10th anniversary of the terror attacks in the United States.
To applause from the crowd at Arthur Ashe Stadium, the Spaniard added: “Tomorrow is a very tough day for all the poeple in New York, so I offer all my support to the families of the victims. I really have terrible memories of that day.”