Head coach Zinedine Zidane made some changes to Real Madrid's normal starting line-up, with Luka Modric and Isco left on the bench at the outset at Santiago Bernabeu stadium and Gareth Bale, Eden Hazard and Marcelo also missing due to injury.
Vinicius Junior stepped up as key figure in the first half for Real Madrid on Saturday, who typically suit up in white at home but instead wore their alternate green uniforms in support of the ongoing climate summit in the Spanish capital, reports Efe news.
The Brazilian forward - making his first start since October 19 - put constant pressure on Espanyol's defense over the first 45 minutes, creating numerous chances that he was unable to convert against visiting net minder Diego Lopez.
Real Madrid, however, managed to break through Espanyol's defensive wall at the 37-minute mark when Benzema drew a crowd of defenders and passed the ball off to Varane, who slotted a left footed shot just inside the far post.
The second half began with a flurry of action, as Benzema was denied by Lopez in one clear opportunity in the 53rd minute before Espanyol's Wu Lei hit the woodwork with a shot two minutes later.
But instead Real Madrid put the game out of reach when Benzema received a cross from Federico Valverde and struck a shot between a defender's legs and into the back of the net in the 79th minute.
The Blancos' Ferland Mendy was sent off for a second yellow card four minutes later, but it was far too late for Espanyol to capitalize.
With the win, Real Madrid (34 points) provisionally jumped back into first in LaLiga ahead of arch-rival FC Barcelona, although the Catalans (31 points) will have a chance to retake the top spot when they take on Mallorca.