A Gareth Bale strike and late double from Alvaro Morata proved to be enough for hosts Real in their final game of the domestic season, despite Pizzi's consolation for Espanyol, but the victory was marred by setbacks to Cristiano Ronaldo and Karim Benzema.
Ronaldo, who limped off with a muscle injury in the 1-1 draw at Real Valladolid earlier this month, sustained a problem in the warm-up and was replaced in the side by Isco, placing his participation in next weekend's Champions League showpiece with city rivals Atletico Madrid in doubt.
And the nine-time European champions could also be without Benzema for the clash in Lisbon after he came off in the 67th minute with an apparent groin complaint.
Real were always in control and ensured victory with a late flurry from Benzema's replacement Morata, but the focus will firmly be on the prospects of their injured attacking pair prior to the showdown with Atletico and next month's FIFA World Cup.
The hosts took a while to find their rhythm without Portuguese talisman Ronaldo, the first real chance taking 13 minutes to arrive as Benzema headed over Marcelo's left-wing cross.
Marcelo then forced Kiko Casilla into a near-post stop with a shot from a tight angle before Sergio Ramos drew another save from the Espanyol goalkeeper from the resulting corner.
Ramos, scorer of five goals in his last six games, continued to show signs of potentially adding to his tally, firing narrowly wide from long range in the 27th minute.
But the best chance of the first half fell to Benzema, who cleverly worked his way past a couple of defenders inside the area only to be denied by a fine Casilla save.
Yet for all their dominance, Real may have fallen behind had Daniel Carvajal not produced an excellent last-ditch tackle to prevent Simao from getting a shot away from point-blank range.
Real cut the look of a frustrated side for much of the encounter as they laboured to try and find a way through a stubborn Espanyol defence, with Ramos once again going close as he curled over in the 63rd minute.
However, Carlo Ancelotti's men finally found the back of the net just a minute later when Bale raced onto Benzema's clever reverse throughball and slotted in off the post.
Espanyol missed a glorious chance to level almost immediately, Simao somehow missing the target when one-on-one with Iker Casillas.
Morata effectively made sure of the points with a close-range finish in the 86th minute before Pizzi converted Sergio Garcia's neat pass to halve the deficit.
A second for Morata put the gloss on a straightforward win, but that will have done little to calm the tension surrounding the fitness of Ronaldo and Benzema.
