Almagro played more than 2 hours in getting past Santiago Giraldo 7-6 (7-4), 6-7 (3-7), 6-3. The players combined for 25 aces with the difference in the match being Almagro's managing to hold serve through the third set.
No. 4-seeded Marcos Baghdatis took out Bjorn Phau 7-5, 6-2 in earning his quarterfinal slot. Baghdatis had three service breaks, all coming after the 10th game of the first set.
Juan Ignacio Chela, the No. 8-seed, also advanced in three sets with a 2-6, 7-6 (7-5), 6-3 win over Grega Zemlja. Chela managed just one break on the day but that determined the third set.
Other matches Thursday saw Michael Berrer slip past Pablo Cuevas 5-7, 6-3, 6-3; and Andreas Haider-Maurer play 2 1/2 hours in topping Andreas Seppi 6-3, 6-7 (7-9), 7-6 (7-2).
Almagro and Chela will meet in one quarterfinal Friday in the same half of the bracket as top-seeded Jurgen Melzer, who will go against seventh-seeded Philipp Kohlschreiber in his quarterfinal. No. 2-seeded Marin Cilic is paired against Haider-Maurer while Baghdatis plays Berrer in the bracket's lower-half matches.