The 14th seed broke in the eighth game of the final set and served out to secure the victory in four hours, 13 minutes.
"I knew Gilles wasn't going to go away," Cilic said. "It was very hard conditions but I was really focused today and kept in there."
Cilic had lost all four of their previous meetings, all in the deciding set, and when Simon forced a break point in the first game of the fifth, the Frenchman looked like the favourite to win again.
But Cilic saved it and then after breaking for 5-3, he held his nerve to set up a clash with either Czech sixth seed Tomas Berdych
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