Jese Rodriguez scored the only goal of the return leg in the seventh minute as the Bernabeu faithful were subjected to a lacklustre performance by the home side, who made changes but still had the likes of Cristiano Ronaldo, Xabi Alonso and Sergio Ramos in the starting XI.
However, as long as the lead remained at two goals Espanyol were always in with a chance, particularly against an off-colour Madrid, but the 77th-minute dismissal of Victor Sanchez for a second yellow card finally took the fight out of the visitors.
The win completes one half of a possible all-Madrid semi-final, with Atletico in line to meet Carlo Ancelotti's men in the final four should they complete the job against Athletic Bilbao on Wednesday, having won the first leg 1-0.
In the other half of the draw, Barcelona look all but assured of their place in the semi-finals as they host Levante on Wednesday holding a 4-1 lead from the first leg.
Barring a massive upset, Gerardo Martino's men - looking to win the cup for a record 27th time - will meet either Real Sociedad or Segunda Division side Racing Santander in the last four.
Sociedad hold a 3-1 lead as they make the short trip to Cantabria on Thursday to face Racing, who are the only non-Primera Division club left in the competition.