Top-seeded Tipsarevic through in Bucharest
Tipsarevic dropped serve just once and saved eight of the nine break points he faced, while breaking Giraldo four times.
"I don't think it was an easy game, despite the score," Tipsarevic said.
Guillermo Garcia-Lopez of Spain will face Tipsarevic after defeating Sergiy Stakhovsky of Ukraine 1-6, 6-3, 6-4.
Also, Romania's Victor Hanescu topped fourth-seeded Mikhail Youzhny of Russia 6-4, 6-3 without losing his serve, and No. 5 Florian Mayer defeated David Goffin of Belgium 7-6 (2), 1-6, 6-3. Hanescu will play Mayer on Friday.
The other quarterfinals feature defending champion Gilles Simon playing Daniel Brands, and eighth-seeded Viktor Troicki against Lukas Rosol.