Troicki broke early in each set and again at 5-2 in the second. He will play either second-seeded Marin Cilic or Antonio Veic after their all-Croatian quarterfinal.
Stakhovsky, who had only three break points, had knocked out Troicki in the second round of last year's tournament.
Jan Hernych of the Czech Republic advanced when Mischa Zverev of Germany retired citing breathing problems while trailing 5-4 in the first set. Hernych will play the winner of another all-Croatian match, seventh-seeded Mario Ancic against qualifier Ivan Dodig.
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Troicki beats 2008 champ Stakhovsky in Zagreb
