Cilic held serve throughout the match and saved three break points at 1-2 in the second set before coasting to victory.
Ivan Ljubicic, also of Croatia, crushed Christophe Rochus of Belgium 6-4, 6-1 in just 57 minutes.
The victory extended Ljubicic's strong form in Zagreb where he won the inaugural tournament in 2006 and was the finalist in 2007 and 2008.
Ljubicic broke Rochus early and the Belgian briefly recovered to come back to 4-5 in the first set, but managed to win only one more game in the match.
Teimuraz Gabashvili of Russia beat countryman Mikhail Youzhny 6-3, 6-4 to advance. Youzhny failed to convert any of his seven break points before bowing out.
Another of the nine Croatians in the tournament Antonio Veic, the 20-year-old who is ranked No. 255 in the world, upset veteran Guillermo Canas of Argentina 4-6, 6-4, 6-2. Canas received medical attention for arm injury during the match.
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