A Liga defeat to Valencia last weekend was followed up by a Copa del Rey loss at bitter rivals Atletico Madrid on Wednesday but, although Fabio Coentrao was sent off early in the second half, Real never looked at risk of losing three games in a row for the first time since 2009.
Karim Benzema provided Espanyol with an early warning at the Santiago Bernabeu as he blasted against the post after just 10 minutes, and the breakthrough followed shortly after as James Rodriguez found the net following Cristiano Ronaldo's assist.
The FIFA Ballon d'Or nominee then watched on as Gareth Bale doubled Real's lead with a fine free-kick in the 28th minute.
The hosts' position was put in doubt seven minutes into the second half as Coentrao received a red card following a forceful collision with Jose Canas.
Yet Espanyol struggled to make the most of their numerical advantage and Real ultimately added a third through substitute Nacho Fernandez, as they moved four points clear of Barcelona and Atletico Madrid - who meet on Sunday - at the top of the table.
Espanyol started the contest brightly and created two chances inside the first three minutes, Felipe Caicedo scuffing wide after a clever run and Sergio Garcia firing straight at Iker Casillas from 20 yards.
Real soon clicked into gear, though, and Benzema went extremely close in the 10th minute, striking the post with a fierce half-volley.
The goal frame failed to save Espanyol a few moments later as Real took a deserved lead through Rodriguez, who steered home after receiving Ronaldo's well-placed cut-back.
Real continued to dominate after taking the lead and, although Raphael Varane headed a presentable chance wide in the 16th minute, Carlo Ancelotti's men did not have to wait much longer before doubling the deficit.
Bale stepped up ahead of usual free-kick taker Ronaldo just before the half-hour mark and sent an unstoppable effort in off the right-hand post from 30 yards, leaving goalkeeper Kiko Casilla helpless.
Real were not given an ideal start to the second half as Coentrao was controversially dismissed after Canas and the Portugal international had crashed into each other with 53 minutes on the clock.
However, the sending off had little impact and Ronaldo almost netted Real's third shortly after, shooting narrowly wide of the bottom-left corner from the edge of the area.
Real did wrap things up eventually, as Nacho - introduced in response to Coentrao's red card - slammed a half-volley past Casilla following Alvaro Arbeloa's dinked cross 14 minutes from time.
Victory sees Real provide the response Ancelotti had demanded following the defeats to Valencia and Atletico, while also putting the pressure back on Barca ahead of their showdown with the champions on Sunday.
