Starace, who beat Chela in three sets in the Croatia Open semifinals last year, ousted him in 2011 with a 6-4, 4-6, 7-5 score. He converted all three of his break-point opportunities in the third set.
Starace heads to the quarterfinals against sixth-seeded Fabio Fognini, who was a 6-4, 6-1 winner over Olivier Rochus earlier Thursday. Fognini won 57 percent of the points in the match -- 55 percent off Rochus's serve -- and had six breaks in nine receiving games.
Local favorite Marin Cilic, the No. 4 seed, earned his quarterfinal spot with a 4-6, 6-4, 6-3 victory over Robin Haase. He dropped serve just once after the first set.
Seventh-seeded Andreas Seppi, who defeated Diego Junqueira 7-5, 6-1, claimed the other quarterfinal berth and will play Cilic Friday. Seppi won 60 percent of the points in putting the match away in the second set.
Friday's other quarterfinal pairings have second-seeded Alexandr Dolgopolov playing Albert Ramos while defending champion Juan Carlos Ferrero meets Carlos Berlocq.