Rios is looking for his first title of the year and 19th overall. His best results of the season were semifinal finishes at the Tennis Masters Series event in Miami and the Washington hardcourt tournament.
The Chilean next will take on sixth-seeded Davis Sanchez of Spain, who recovered from a poor first set to breeze past Jurgen Melzer of Austria, 3-6, 6-1, 6-1. Sanchez, who lost his only previous match against Rios in the quarterfinals at Umag in 2000, reached his first tour semifinal in Bucharest and finished runner-up in a Challenger at Szczecin.
Third seed Jose Acasuso of Argentina moved closer to his third final of the year Thursday with a 6-4, 7-6 (7-5) victory over Nicolas Coutelot of France. Acasuso, 19, won his first ATP title at Sopot in July and appeared in the final at Bucharest earlier this month.
"I am very confident," Acasuso said. "This is not my last chance to win another title this year. I can also play good on indoors. I just have to go step-by-step."
Acasuso will face Peru's Luis Horna in Friday's quarterfinals. Horna routed fifth seed David Ferrer of Spain, 6-1, 6-2, to reach the final eight of a tour event for the first time in his career. He won three Challenger titles this year, prevailing on the clay courts at Zagreb, Furth and Weiden.
"I'm surprised mostly by the score," Horna said. "I hope I can continue with this good game, maybe I've been lacking consistency."
"I don't really know what happened, I just lost very badly," said 20-year-old Ferrer, who won his first career title at Bucharest. "I'm still in a learning process, this is only my fourth ATP event."
Also, Armenia's Sargis Sargsian defeated Costa Rican qualifier Juan Antonio Marin, 6-2, 7-6 (7-4), and Bohdan Ulihrach of the Czech Republic beat Brazil's Fernando Meligeni, 7-5, 6-3.
Gonzalez, the second seed from Chile, cruised past Spaniard Albert Montanes, 6-4, 6-4 to advance to a meeting with Martin. On Tuesday, the 22-year-old Gonzalez beat Croatian Zeljko Krajan before rain suspended play.
Gonzalez won his first career title in February at the Vina del Mar in his native country.
Sixth seed David Sanchez of Spain joined Rios in the second round. Sanchez had a 6-2, 2-0 lead when Frenchman Richard Gasquet retired due to a viral infection.
Luis Horna of Peru defeated German qualifier Marcello Craca, 6-4, 4-6, 6-1, in another first-round match that began Tuesday.
Elsewhere, Sargis Sargsian of Armenia ousted Italian qualifier Filippo Volandri, 4-6, 7-6 (7-5), 6-1; Fernando Meligeni of Brazil posted a 6-2, 5-7, 6-2 win over Bohdan Ulihrach of the Czech Republic; and Costa Rican qualifier Juan Antonio Marin defeated Italian Stefano Galvani, 7-6 (7-4), 6-4.