Djokovic, chasing the only grand slam title to elude him, was in complete control until the end of the third set, when the big-serving Cilic forced him to a tiebreak, which the six-times grand slam champion lost 7-2.
Normal service resumed afterwards and Djokovic, although not playing his best tennis, finished it off on Cilic's serve when the Croatian double faulted.
He will next face either Frenchman Jo-Wilfried Tsonga, the 13th seed, or Polish 22nd seed Jerzy Janowicz.
(Reporting by Julien Pretot; Editing by Toby Davis)
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