Cilic won this tournament in 2009 and 2010 and improved his record at the event to 14-4. He had 11 aces and broke his opponent three times.
"I am very pleased with the way I played," Cilic said. "I felt he was nervous in the beginning and it helped me gain an early advantage."
Cilic will face another Slovenian, Blaz Kavcic, who upset sixth-seeded Marcos Baghdatis of Cyprus 3-6, 7-6 (2), 6-4 and reach his third career quarterfinal. Baghdatis, the 2007 champion, failed to serve out the match at 5-4 in the second set, and pulled out of the doubles because of a foot injury.
"I did not want to take any risks," he said. "I have to give credit to Kavcic, he played well."
Ivan Dodig also reached the quarterfinals by defeating Ivo Karlovic 7-6 (2), 6-7 (2), 6-3. Dodig wasted a match point at 5-4 in the second set, allowing Karlovic his only break.
Dodig will play defending champion Mikhail Youzhny on Friday.
Fourth-seeded Jurgen Melzer of Austria rallied past Somdev Devvarman of India 1-6, 7-6 (5), 6-2. Devvarman had a 5-3 lead in the tiebreaker, but then lost four points in a row.
Robin Haase of the Netherlands defeated fifth-seeded Martin Klizan of Slovakia 6-2, 4-6, 6-4.
Also Thursday, Lukas Rosol of the Czech Republic ousted Italy's Flavio Cipolla 6-4, 2-6, 6-3 and Philipp Petzchner of Germany beat Croatian wild card Dino Marcan 6-3, 6-4.