Fognini saved the only break point he faced and converted two of his six chances to beat the seventh-seeded Giraldo in 81 minutes,
The top-seeded Italian, who is bidding to reach his fourth final of the season, next faces the third-seeded Roberto Bautista Agut, who beat Spanish compatriot and No. 6 Guillermo Garcia-Lopez 3-6, 6-4, 7-6 (1).
Lukas Rosol upset the fourth-seeded Feliciano Lopez of Spain 4-6, 6-3, 7-6 (4). The 48th-ranked Czech next faces No. 2 Mikhail Youzhny of Russia. The 2002 tournament winner defeated Argentina's eighth-seeded Federico Delbonis 7-6 (2), 6-2.
Youzhny won 74 per cent of his service points and saved the three break points he faced for victory in 1 hour, 41 minutes.