The 33-year-old Cilic won on Wednesday evening in Paris against the Russian Rublev in Super Tiebreak with 5: 7, 6: 3, 6: 4, 3: 6, 7: 6 (10: 2).
After 4:10 hrs, the 2014 US Open Champion utilized its very first match ball.
In the last quarter-final game, Norwegian Casper Ruud as well as Holger Rune from Denmark are still facing each other in the night.
Alexander Zverev had already reached the semi-finals on Tuesday by winning Carlos Alcaraz.
There the Olympic champion meets the 13-time Paris champion Rafael Nadal on Friday.
The Spaniard had actually dominated versus safeguarding champion Novak Djokovic from Serbia.