Nadal has won nine Grand Slam titles during his astonishing career but the Spaniard has never triumphed at this prestigious end-of-year event featuring the world's top eight players.
Now he has a golden opportunity to end a remarkable season with one last triumph at London's O2 Arena.
The world number one, who has already won Wimbledon and the French and US Opens this year, will play Roger Federer or Novak Djokovic in Sunday's final.
Nadal said: "Today I played one of the finest matches of my career. Andy came back well. In the tie-break the only thing I could do was wait for chances.
"I want to congratulate Andy for his attitude. He's going to win a lot of grand slams in my opinion."
Defeat was hard on Murray, who led 4-1 in the final set tie-break, and even the consolation of taking part in one of the best matches of the year couldn't completely ease the Scot's frustration.
"It was a great match. I think both of us played very well. I probably played one bad game the whole match or maybe just a couple of bad points," Murray said.
"I knew when I was out there that it was a great match, the noise the crowd made when we changed ends at six-all was pretty incredible.
"It's nice in some ways to be involved in matches like that. But it's not nice losing them."
Murray knew he had to improve his serving to compete with Nadal and the early signs were good there, too, as he fired down seven aces in his opening four games, losing only four points in the process.
Neither player was prepared to give an inch and the set proceeded smoothly all the way to the tie-break, which Nadal took after a gruelling battle for supremacy.
Murray faced two break points early in the second set. Now was the time for the Scot to show his fighting spirit, and he did, with a brave second serve saving one before a backhand winner took care of the second.
The crowd sensed that could prove a big moment and in the seventh game Murray got his chance.
A gift from Nadal was followed by two terrific points from the home hope to take him to 0-40.
Nadal saved all two of those break points but he then missed a backhand to give Murray a third chance, and this time he took it, leaving his opponent standing with a searing cross-court backhand.
Serving to stay in the set at 3-5, the Spaniard was left helpless as Murray blasted his way to 15-40 and then drilled a backhand winner cross-court to level the match.
Early in the third set, Murray turned to the drop shot, but it let him down badly and, out of nothing, Nadal broke serve.
Murray created two more break points at 2-3 only for the world number one to serve his way out of trouble, and at 3-5 Nadal had match point.
For once the Spaniard could not find the shot for the occasion, overcooking a forehand return, but he still had a chance to serve for the match.
In a contest as dramatic as this, it was inevitable there would be another twist, and so it proved as Murray moved to break point, which he took with a stunning backhand pass.
That sent the match to a decisive tie-break and Murray who made the early move, two mini-breaks putting him 3-0 ahead.
Back came Nadal though and at 5-6 the Spaniard had another match point.
Murray saved that one but on Nadal's serve moments later, after three hours and 11 minutes, the match was finally decided with a superb winner from the Spaniard.