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Top seed Djokovic, playing his first ATP event while holding the top ranking, will await a winner from French fifth seed Gael Monfils and Serb Viktor Troicki.
Djokovic went through in 95 minutes in the third-round contest to notch up his sixth victory over Cilic, a one-time member of the Top-10 now standing at 29th.
Djokovic earned the opening set on a late break and took a 3-1 lead in the second to pave the way to his 50th win of the season against just one loss to Roger Federer in the French Open semi-finals.
The near-unstoppable Serb is bidding for a ninth title this season as he plays at the event where he won on his debut in 2007. He went out in the semi-finals a year ago to Federer.
Czech seventh seed Tomas Berdych defeated huge Croatian server Ivo Karlovic 6-3, 7-6 (7/2) and next faces either Serb Janko Tipsarevic or Croatian Ivan Dodig, a surprise winner in three sets over the second seeded Rafael Nadal on Wednesday.
Third seed Federer will play later on in a re-run of a Wimbledon quarter-final, taking on 13th seed Jo-Wilfried Tsonga.
The Frenchman beat the Swiss in a Wimbledon quarter-final this summer and also clocked a victory in the series here in 2009.
