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."
Dodig will play defending champion Mikhail Youzhny on Friday.
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. Marcan entered the tournament as a replacement for second-seeded Andreas Seppi, who withdrew because of an illness.