The hosts started brightly and should have been ahead within 12 minutes but Raul Baena smashed a volley wide from only six yards out.
Baena though made amends as he headed in from Thievy Bifouma's flick-on after 26 minutes and Espanyol doubled their advantage just before half-time as Allan Nyom was harshly penalised for a trip on Vladimir Weiss and Joan Verdu slotted home the penalty.
The visitors improved after the break but were too often wasteful with their final ball and Espanyol wrapped up the points when Rui Fonte fired in after Julio Caesar had parried Ndri Romaric's free-kick.
The hosts had come into the game short on options in attack as Sergio Garcia and Alvaro Vasquez picked up serious injuries this week. However they made light work of their absence as they controlled the game from the off.
Romaric's powerful drive was beaten away by Caesar but from the rebound Baena inexplicably tried to lash the ball home from close range and pulled his effort wide.
The midfielder though did get his first goal of the season 14 minutes later as Thievy's near post header from a corner found him all alone at the back post for the simplest of finishes.
Granada had offered almost nothing as an attacking force in the first quarter but they had a great chance to equalise as sloppy play in midfield by the hosts allowed Dani Benitez to be played through on goal, but he placed his shot too close to Kiko Casilla and the keeper diverted the ball away with his legs.
Yet just as Granada had started to pose a threat they fell further behind as Weiss turned inside the area and was adjudged to have been tripped by Nyom. The Cameroonian received a yellow card for his vehement protestations but Verdu kept his composure to send Caesar the wrong way from the spot.
Granada enjoyed more possession in the second-half but other than a routine Casilla save from Nyom's shot, they did not really threaten to find a way back into the game.
And their misery was complete 10 minutes from time when Caesar did well to parry Romaric's fiercely struck free-kick, but the ball fell kindly for Fonte to hook into the empty net.