A brace from Karim Benzema and one each for James Rodriguez and Marco Asensio saw Zinedine Zidane's side return to winning ways in impressive fashion, and leave the Madrid giants two points clear at the top of the division.
Gareth Bale missed out for Real Madrid as he started his two-game suspension, while Cristiano Ronaldo was not selected due to a muscular problem, leaving Lucas Vazquez and Asensio alongside Benzema in the final third.
As for Eibar, French defender Florian Lejeune missed out through suspension, meaning that there was a spot in central defence for Mauro dos Santos, while Sergi Enrich also returned to the team at centre-forward.
Neither side created much of note in the early exchanges, with a Dos Santos header, which dropped into the arms of Keylor Navas, the closest that either team came to breaking the deadlock in the opening 10 minutes of action.
Real Madrid made the breakthrough in the 14th minute, however, when Benzema swept the ball home from close range after seeing his initial effort saved by Eibar goalkeeper Yoel, who had no help from his teammates.
Benzema then doubled Los Blancos' lead 11 minutes later when he made contact on a deep free kick from James and the ball found a route past the helpless Yoel once again.
It went from bad to worse for Eibar in the 29th minute when James converted a Benzema cross into the top corner to send Real Madrid into a commanding three-goal lead entering the latter stages of the first period.
Eibar's best chance of the first half arrived six minutes before the break when Enrich turned inside the Real Madrid box before firing the ball towards the bottom corner, but Navas was on hand to make a smart save.
Asensio and Benzema came close to scoring a fourth for Real Madrid in the latter stages of the opening 45 minutes, but the former's curling effort just missed the far post, before the latter was denied a first-half hat-trick by Yoel.
Asensio had a half-chance for Los Blancos just before the hour after breaking into the Eibar box, but Ivan Ramis was across to make a smart block as the hosts looked to limit the damage that they had suffered in the first period.
Asensio was not to be denied, however, and scored Real Madrid's fourth of the afternoon on the 60-minute mark when he converted from inside the box after James had seen his effort clip the outside of the post.
Eibar thought that they had a consolation in the 68th minute when Gonzalo Escalante converted from close range, but the offside flag prevented the home supporters from having something to cheer.
Isco joined Mariano Diaz and Mateo Kovacic on the field as Zidane used all three of his substitutions in the second period, but it was Eibar that continued to dominate the ball as they looked to score an unlikely second goal.
Real Madrid closed out the match in the final moments, however, as Zidane's team ensured that they would return to the top of the table ahead of Barcelona, who host Celta Vigo on Saturday night.
Real Madrid will now travel to Napoli on Tuesday night looking to secure their spot in the quarter-finals of the Champions League, before returning to La Liga action at home to Real Betis on March 12. Next up for Eibar, meanwhile, is a trip to basement side Osasuna on March 13.