And champions Atletico Madrid remain four points off the top as they overcame Malaga 3-1 at the Vicente Calderon thanks to goals from Tiago, Antoine Griezmann and Diego Godin.
Real Madrid enjoyed a comfortable afternoon in unfamiliar surroundings on their first league visit at the 5000 capacity Ipurua stadium in Eibar.
The European champions had more than a touch of fortune in the first half as James Rodriguez headed home the opener despite Ronaldo and Karim Benzema appearing to be in an offside position in the build-up to the goal.
Ronaldo then doubled the lead himself with a mishit shot that looped beyond Xabi Irureta just before the break.
Benzema smashed home the third 20 minutes from time before Ronaldo rounded off the scoring from the penalty spot.
"The objective is to continue with this run because the team is playing well and the players are motivated," said Real boss Carlo Ancelotti.
"But the season is very long and we need to continue with this type of attitude."
AFP rj
-AAP