The hosts took the lead after 16 minutes when Jonathan Viera advanced into the box before slotting his effort underneath the keeper.
Sergio Garcia almost put the visitors into the lead 10 minutes after the break when he collected the ball inside the box, but his effort was pushed away by the keeper.
Alvarez was called upon again 10 minutes from time, this time to deny Jonas's strike from the edge of the box.
The hosts were handed the perfect chance to score a late winner when they were awarded a penalty in the 86th minute, much to the dismay of the Espanyol players. During the protests both Hector Moreno and Sergio Garcia were shown red cards, reducing the visitors to nine men.
Soldado eventually stepped up to the spot kick and made no mistake to give his side all three points.