It took Cilic 110 minutes to see off the challenge of Stakhovsky.
In a doubles match, at the outside court, German pair of Andre Begemann and Martin Emmrich survived some anxious moments before prevailing over the English duo of Jamie Delgao and Ken Skupski 7-6 (1) 6-1 in 64 minutes.
They will meet the winner of the match between Somdev Devvarman/Stakhovsky and Thailand's Sonchat and Sanchai Ratiwatana.
In another match at the outside court, fifth seeded Benoit Paire of France thrashed Israeli Dudi Sela 6-1 6-0 in just 40 minutes, extracting a sweet revenge for his last year's defeat to the same opponent. In his quarterfinal match tomorrow, Paire will take on favourite Cilic.
After being broken in the very first game of the first set, Cilic, who had won the title here in 2009 and 2010, dished out flawless tennis in the next two games.
Cilic, world number 15 and seeded third here, was defeated by Kei Nishikori of Japan 4-6 6-3 6-2 in the quarterfinals satge in 2011. The Croat had not competed last year.
With his rival holding on to the service games, Stakhovsky maintained great accuracy and brought his forehand drives into play. The Ukrainian earned two game points with a brake in the seventh game.
In the eighth, Stakhovsky, despite committing two double faults, managed to win the game. In the second and third games, Cilic was at his best as he relied on the long baseline rallies for points.
