The visitors thought that they had taken the lead in the opening 10 minutes when Borja Fernandez found the back of the net, but a foul by Raul Navas in the build-up resulted in the strike being chalked off.
There was a disallowed goal for the hosts a few minutes later as Javier Hernandez turned the ball in from close range, but the on-loan Mexico international was offside.
Real did manage to get a goal on the board with just over 20 minutes played when Cristiano Ronaldo stepped up to blast in a free kick, with the movement on the ball sending Xabi Irureta in the wrong direction.
The hosts doubled their lead before the break as Hernandez got forward again, this time staying on side to head in from an Alvaro Arbeloa cross.
The hosts continued to look the more likely going forward in the second half as Marcelo raced down the wing before crossing it in for Jese Rodriguez, but his strike was straight at the keeper.
Hernandez looked for a second as Arbeloa set him up again with another cross into the Eibar box, but the Mexican’s header did not trouble the visiting keeper.
Hernandez and Ronaldo both missed chances to secure a third for Carlo Ancelotti’s side, but the hosts finally added to the score in the final 10 minutes when Jese Rodriguez rounded a couple of defenders before squeezing it in from a tight angle.
Isco could have made it four for the hosts just a couple of minutes later a Eibar left themselves wide open at the back, but the keeper remained alert to make the save.
The result leaves Los Blancos two points behind Barcelona, who could only manage to draw 2-2 at Sevilla, while Eibar stay 14th.
