Kohlschreiber, the No. 8 seed, defeated Almagro 7-6 (7-5), 6-4 in a very tight match. Almagro won more points -- 70-69 -- overall but Kohlschreiber saved the only two break points he faced.
He won just seven points off Almagro's serve in the second set but that was enough to get the match's only break.
Olivier Rochus just got by qualifier Benoit Paire 6-3, 6-7 (5-7), 7-6 (7-4) in the only other match completed Thursday. Paire had 21 aces but Rochus advanced with a more finesse style of play. Rochus faces Kohlschreiber in the semifinals.
Thursday's other matches were rained out and are set for Friday, with the semifinals also scheduled. Top-seeded and defending champion David Ferrer is to play Alejandro Falla in one quarterfinal and No. 3-seeded Fernando Verdasco is to face Guillermo Garcia-Lopez in the other.