Gareth Bale curled in a 20-yard free-kick, off the post, to double the lead. Left-back Fabio Coentrao was sent off for a sliding tackle but it mattered little as Nacho slotted in the third.
Carlo Ancelotti’s side are four points clear of nearest rivals Barcelona and Atletico Madrid, with at least one of those sides poised to drop points when they meet in Catalonia on Sunday.
Real, who will have played a match fewer than their title rivals after the Nou Camp clash, have taken control of La Liga on the back of 12 successive wins.
Last Sunday’s 2-1 defeat at fourth-placed Valencia ended their Spanish record run of 22 victories in all competitions, before they tumbled to another loss at neighbours Atletico in the Copa del Rey.
However, Italian boss Ancelotti insisted there was no cause for concern – and so it proved against mid-table Espanyol.
Rodriguez finished a classy move which saw Cristiano Ronaldo instantly pull back Bale’s sublime cross-field pass into the Colombia midfielder’s path.
Espanyol keeper Kiko Casilla was rooted to his spot as Bale whipped in the second, before Portugal defender Coentrao was harshly shown a red card after lunging into a 50-50 tackle.
But Espanyol could not take advantage of their extra man, with Spain defender Nacho drilling in Alvaro Arbeloa’s left-wing cross at the far post for the third.