While victory would have been a significant boost to their Champions League aspirations, they may have left the Cornella-El Prat thankful for a point as Javi Lopez's own-goal 14 minutes from time denied the hosts maximum points.
It was the second time Sociedad had come from behind in the match, David Zurutuza scoring either side of strikes from Sergio Garcia and Christian Stuani in a busy first half.
Garcia gave Espanyol the lead with the first decent opening of the game in the ninth minute.
Simao was the provider with a ball into the six-yard box, with Garcia providing the right-footed finish across Enaut Zubikarai.
Simao was soon causing trouble again, his cross forcing the goalkeeper to punch clear moments after the restart.
Sociedad took their time in fashioning a response but levelled in the 23rd minute.
Zurutuza was the man on target, rifling a 25-yard effort past Francisco Casilla.
Espanyol ensured a half-time lead in the 38th minute when Garcia turned creator.
His ball from the left channel found Stuani in a central position and the Uruguayan finished from 12 yards.
Both sides were lively after the break, Antoine Griezmann shooting wide for the visitors before Victor Sanchez responded in kind for Espanyol.
The rival keepers were then called on, Casilla denying Imanol Agirretxe with his feet and Zubikarai parrying a Joan Verdu effort.
Agirretxe found Casilla on form again after 62 minutes, the latter diving to paw the ball round the post.
It looked like Sociedad might not have the necessary firepower to get back into the game but as it was, they did not need to provide their own finishing touch.
Instead, Griezmann's cross was met by Lopez, who mistakenly directed the ball over his own line.
There were scant opportunities for a winning goal as both sides accepted a share of the spoils.