It was a milestone for the Wimbledon champion, who reached the semifinal level for the first time since undergoing back surgery in September.
After losing the first set on the clay courts of Acapulco, Murray came from behind to take the second set and then broke Simon at love in the final game to notch a 1-6, 7-6 (4), 6-2 victory.
Alexandr Dolgopolov of Ukraine advanced with a 6-5, 7-6(4) win over Ivo Karlovic. Seventh-seeded Ernests Gulbis and fourth-seeded Grigor Dimitrov of Russia were locked in a three-set battle for the remaining semifinals berth late Thursday.
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