Playing in his first tournament since winning the U.S. Open last month, the top-seeded Briton won on the back of his powerful forehand and some fine volleys.
Murray will play sixth-seeded Milos Raonic of Canada on Saturday. Raonic outlasted third-seeded Janko Tipsarevic 6-7 (5), 6-2, 7-6 (7) in a match that took nearly 2 hours, 45 minutes.
Unseeded Marcos Baghdatis of Cyprus joined Murray and Raonic in the semifinals by defeating Russian qualifier Dmitry Tursunov 6-2, 6-4 in the quarterfinals.
Second-seeded Tomas Berdych of the Czech Republic will take on local favorite Kei Nishikori, seeded eighth, later Friday in another quarterfinal.
“It was tough. I started the match well,” said Murray. “Stan came back at the beginning of the second set. There were a lot of long games, long rallies.
He won them in the second second and I took them in the third. Tough games.”
The third-ranked Murray broke Wawrinka in the opening game of the match, but had to battle to hold serve in the next game, staving off three break points.
Murray, who beat Wawrinka in the first round on the way to winning the gold medal at the London Olympics, came to the net successfully several times in the first set and broke again with an overhead smash after a lengthy rally to take a 4-1 lead. He closed out the set with an ace.
Wawrinka, ranked 16th, broke Murray in the fourth game of the second set to move ahead 3-1. Playing primarily from the baseline, the Swiss hit several winners to level the match.
Murray broke in the fourth game of the third set to take a 3-1 lead, after Wawrinka had saved three break points.
Murray's deep returns and some timely passing shots proved decisive in the final set as he closed out the match with another break.
Seeking his fourth title of the season, Murray is expecting a challenge on Saturday against Raonic.
“It will be different than today. He has a massive serve, so there won't be many rallies,” said Murray. “He is always a tricky player because of his game style.”
Raonic closed out a hard-fought victory with his 24th ace of the contest.
The match was just the second between the two players. The first was a marathon lasting 3 hours, 14 minutes in Chennai, India, earlier this year that the Canadian won in a third-set tiebreaker following 36 games without a single service break.
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