Top-ranked Rafael Nadal plays fifth-seeded Gael Monfils later in the other semifinal.
Despite nursing a minor injury to his right foot, Murray dispatched the two-time ABN Amro champion in just over an hour. He broke the Croat's serve in the second game of the first set and first game of the second.
"I hope I end up facing Rafael Nadal in the final," Murray said. "Our matches are usually guaranteed to be a spectacle."
Murray won in Doha, Qatar, and defeated Rafael Nadal and Roger Federer in an exhibition event this year. Murray lost in the fourth round of the Australian Open.
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