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 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.
Elsewhere on Saturday, Valencia were held to a draw and Villarreal and Malaga also shared the spoils.
Valencia coughed up a lead in their 1-1 stalemate at Celta Vigo.
Rodrigo opened the scoring for Valencia with a strike from outside the area, but Celta goalkeeper Sergio Alvarez perhaps should have done better with the 43rd-minute effort.
But the hosts levelled just after the hour-mark as Fabian Orellana scrambled in a corner at the back post.
Valencia are three points adrift of Atletico after the draw, while Celta sit ninth.
At Malaga, the hosts came from behind to earn a 1-1 draw against Villarreal.
The day's other game saw Eibar overcome Getafe 2-1 thanks to goals from Manu del Moral and Ander Capa.
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