More than five years on from their last meeting, both players made impressive starts but the Scot's superior match practice told as he saved a break point in the third game of the match and then broke himself to easily claim the first set.
"Me and Rafa have played so many tough matches over the years... both of us have gone through injury troubles and it's just great to have the opportunity to be with him on court again," Murray said.
Nadal, who was making his first appearance since the Washington Open in August due to a foot injury, added: "Special to be back in a competition... at the same time we haven't played each other in a while. Super happy to be seeing Andy playing at this great level."
The 20-times Grand Slam champion battled valiantly in the second set and saved a number of break opportunities, but it was Murray who secured the crucial break at 5-5 before serving out to secure victory in an hour and 50 minutes.
"For me, this is a comeback. It wasn't a bad match for me. After a long time on a professional court, so positive feelings," added Nadal.
Murray will face Russia’s Andrey Rublev in the final after he defeated Denis Shapovalov 7-6(5) 3-6 6-4 in the other semi-final.
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