The hosts were never threatened, comfortably advancing on the strength of an early tally.
Jese Rodriguez scored the only goal of the game with a swift and solitary counterattack, lashing in at the near post after just seven minutes.
The visitors slowly edged their way back into the game but their attacking was blunt and they had goalkeeper Kiko Casilla to thank for keeping Cristiano Ronaldo out on a number of occasions.
The result - which extended Real Madrid's club record of competitive victories without conceding to eight games - ensured a 2-0 win on aggregate. Real will face the winner of Athletic Bilbao and Atletico Madrid in the last four of the cup.
Carlo Ancelotti made seven changes to the side that beat Granada 2-0 over the weekend, while the Javier Aguirre chose to make just the one alteration to his XI.
The hosts began with their foot firmly on the throttle and made the visitors pay for sloppy concentration. Xabi Alonso's diagonal, lofted through ball caught Joan Capdevila unaware and Jese controlled with his chest before slamming in at the near post past a poorly positioned Casilla.
The Blancos continued to surge forward and Cristiano Ronaldo was a constant menace in and around the 18-yard box. Isco failed to connect to the Ballon d'Or winner's fizzed ball across the box from the left as Espanyol struggled to cope with the relentless pace.
Two saves in particular were key to keeping the hosts just 1-0 ahead midway through the first 45 minutes - Casilla's casual catch of a dangerous chip from Ronaldo was in sharp contrast to his extravagant reflex leap to deny Angel Di Maria a deflected goal.
Sergio Garcia and on-loan attacker Pizzi caused minor problems for the sturdy Blancos back line as the visitors rallied in the last 10 minutes, but they never truly threatened Iker Casillas between the Bernabeu sticks.
The second half was a more tepid affair as the Periquitos failed to find the spark that could rejuvenate the quarterfinal.
Ronaldo continued to be tormented in front of goal, openly laughing with disbelief when his close-range strike skimmed off Casilla's side and flew inches over the crossbar.
The most notable moment of the second half came when Victor Sanchez was given his third red card of the season. Though the actual sending off was harsh - a clearly accidental handball in a 50-50 with Alonso - he had been putting in dodgy tackles all match and it was not a surprise to see him walk.
Ronaldo lashed into the side-netting, probably out of frustration, as the game dragged on with Real Madrid ultimately happy to settle for a 1-0 win on the night.