In a rematch of the 2010 final between the pair, Cilic won a 6-3 6-7(6) 6-3 tussle in two hours and 45 minutes to avenge that loss two years ago.
"We always have tough matches. I would say the level of tennis was high," third seed Cilic told the ATP website.
"In the second set, Misha was playing unbelievable. He saved a match point with an amazing backhand down the line.
"What I was happy about today was that I kept my level going. Even though I lost my serve at the beginning of the third set, I got the momentum back and I think that was really crucial."
Cilic will next play Tommy Haas who continued his resurgent run with a 6-1 7-6 (3) victory over eight seed Marcos Baghdatis.
Second seed Feliciano Lopez also moved into the last four with a 6-4 6-2 victory over fifth seeded Australian Bernard Tomic .
Lopez will next face Germany's Philipp Kohlschreiber who defeated qualifier Marinko Matosevic 6-0 7-6 (5)