The world number two from Spain, playing his first ATP tournament since facing defeat in the US Open final last month, relied on his powerful baseline game to score a 7-5, 6-1 victory.
Second seeded Murray, fresh from victory at the Thailand Open a week ago, breezed past 2007 champion David Ferrer 6-2, 6-3 to book his place in Sunday's final.
"I hope that I can play a fantastic match (in the final)," Nadal, 25, said after his victory.
"My opponent will be very difficult, so I have to play my best match if I want to win the tournament with the title.
"But for me, being in the final here is a very, very good result. I'm very happy about it. I'll just try to do my best and enjoy a difficult match," added the top seed.
The decisive point came in the 11th game of the first set which had until then gone with serve and was poised at 5-5.
Fish saved the first break point of the match with a winner from a backhand approach, but his stroke on Nadal's next advantage point was short, allowing the Spaniard to batter a forehand winner beyond him for 6-5.
It was enough for Nadal to take the first set. He then took the following five games as the American's resolve deserted him.
The match ended with another break when American fourth seed hit an easy forehand high volley into the net at 30-40 in the seventh game.
"I did a few things better today. I played closer to the baseline. I had a better feeling when I was playing long points from the baseline. When I had a chance, I was able to attack much better than I did yesterday," said Nadal.
Meanwhile, Murray was satisfied with his performance after taking under 90 minutes to dispatch Ferrer.
"I played great from the start to finish. I served very well in the second set and didn't give him too many chances and used a lot of variation on my serves and tried to be aggressive off the first ball of the rally," said Murray.
He predicted a hard battle against rival Nadal acknowledging the Spaniard was playing good tennis.
"He is always tough. He won here last year, so he likes the conditions. I do like them (hard court). I grew up playing on them, so it's surface I feel comfortable on," he added.
Nadal to face Murray in Japan Open final
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