The top-ranked Nadal, who won this year's US Open to complete a career Grand Slam, has never won the season-ending event for the top eight players in the world.
He will face either Roger Federer or Novak Djokovic in Sunday's final at the O2 Arena.
Nadal was solid throughout the first set, but he started to falter after holding serve to lead 3-2 in the second.
Murray won 17 of the next 23 points — and four straight games — to take the set and even the score.
“Today I played one of the best matches of my career,” Nadal said.
Nadal never looked as good after the slump, but he managed to break Murray to take a 2-1 lead in the third set. The Spaniard then had his first match point on Murray's serve while leading 5-3, but the fifth-ranked Briton managed to hold the game, break back to 5-5 and force the final tiebreaker.
In the tiebreaker, Murray won the first three points — two of them on Nadal's serve — and looked like he was going to roll to victory. But Nadal, who also won the French Open and Wimbledon this year, clawed back to 4-4 before getting another match point at 6-5.
Murray again saved that one, but he couldn't do anything about the final match point, which Nadal won with a inside-out forehand.
Murray finished the match with 22 aces, but he also had 47 unforced errors to go along with his 53 winners. Overall, the Briton won 114 points in the match, five more than Nadal.
In the first set, Nadal and Murray traded forehands and backhands but neither allowed the other even one break point.
The second set started much the same, although Nadal did waste the first two break points of the match in the second game. Murray then broke serve to lead 4-3, and then broke again to take the set.
In doubles, Daniel Nestor of Canada and Nenad Zimonjic of Serbia beat top-ranked Bob and Mike Bryan of the United States 6-3, 3-6, 12-10.
