Cilic beat Russian Igor Andreev 6-7, 6-1, 6-4 in two hours and 51 minutes. Cilic fell behind after losing the first-set tiebreak 7-4 before finding better angles to unsettled Andreev on a windswept centre court.
Cilic will next face Italian Andrea Seppi or Albert Montanes. In other fixtures, Jo-Wilfried Tsonga moved into third round with 7-6 7-5 win over Nicolas Almagro.
Sixth seed Fernando Verdasco also moved into round three with a one-sided win over Frenchman Julien Benneteau.
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