Benzema's goal meant Real have come out on top in each of their six games since Christmas, a burst of form that has seen them close the gap to just one point behind Barcelona and Atletico Madrid at the top of La Liga.
Espanyol have a good record against Real in the cup and knocked them out the last time the pair met in the 1999-2000 season, but Carlo Ancelotti's side put themselves in the driving seat with a solid performance.
It was a spirited display from Espanyol but it will take something special for them to turn the tie around at the Bernabeu.
The winners could play holders Atletico Madrid in the semis if they come through their tie with Athletic Bilbao while Barca, on the other side of the draw, face Levante.
