The hosting Catalans dominated large parts of the first half, but they were unable to find a way beyond Roberto in the Granada goal.
When they did manage to beat him, Victor Sanchez saw his powerful effort from inside the penalty area cannon to safety off the crossbar with 12 minutes on the clock.
Their failure to score was eventually punished in the 37th minute when Sanchez brought down Gabriel Torje 20 yards from goal and Benfica loanee Nolito curled the resultant free kick into the net.
Espanyol continued to look the more likely to score during the second half, but once again they could not hit the back of the net.
A cross from Sergio Garcia 13 minutes from time looked to be heading for Christian Stuani, but the Uruguayan was unable to make a firm contact with the ball as Espanyol's best chance of an equaliser was wasted.