The British No1 was 2-0 up in the second set after taking the first 6-4, before his Japanese opponent was forced to quit with a left knee problem.
Murray will take on Bulgarian Grigor Dimitrov, who beat Marcos Baghdatis of Cyprus 6-3 5-7 7-6 (7-5) in the other semi-final, in Sunday’s final.
“I have no idea whether he’ll be nervous or he’ll enjoy the occasion – we’ll find out tomorrow,” said Murray.
“Grigor plays with a lot of variety and he can play a lot of shots. He’s one of the few guys coming through with a single-handed backhand, so he uses a lot more slice.”
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