Los Blancos entered the match down in fourth position after Atletico Madrid had beaten Celta Vigo earlier in the day, but a comfortable win over Eibar has seen the league champions return to third spot.
Real Madrid boss Zinedine Zidane made five changes to the team that started against Tottenham Hotspur in the Champions League on Tuesday night.
Nacho and Theo Hernandez replaced Achraf Hakimi and Marcelo at the back, while Dani Ceballos and Marco Asensio came in for Karim Benzema and Toni Kroos further forward. There was also a change between the sticks as Kiko Casilla replaced the injured Keylor Navas.
As for Eibar, Yoel Rodriguez, Pedro Leon, Fran Rico, Ivan Alejo and Ivan Ramis all missed out through injury. Charles and Takashi Inui came in for Sergi Enrich and Kike in the final third of the field, while there were also starts for David Lomban and Jose Angel as head coach Jose Luis Mendilibar shuffled his pack at the Bernabeu.
It took Real Madrid just two minutes to carve out the first chance of the match, but Isco, after being found by Asensio inside the Eibar box, could not beat Marko Dmitrovic between the away side's sticks.
Eibar had an opportunity of their own in the sixth minute when Charles headed down towards Joan Jordan inside the Real Madrid penalty area, but the midfielder could not find a route past Casilla.
Gonzalo Escalante was next to have a half-chance for the visitors in the 10th minute, although the midfielder's header was never troubling Real Madrid's number two.
For all of Eibar's bright work in the early exchanges, it was Real Madrid that made the breakthrough in the 18th minute when Paulo Oliveira headed an Asensio cross past his own goalkeeper under pressure from Sergio Ramos.
The visitors continued to cause problems, however, with Casilla forced to keep out a Jordan free kick in the 24th minute.
Real Madrid doubled their lead in the 28th minute though, when Asensio swept a low Isco cross into the bottom corner as Eibar conceded a second during a key period of the match.
Los Blancos went in search of more goals in the latter stages of the first period - coming close through Casemiro's long-range attempt, but Eibar were also committing players forward as the visitors continued to impress.
Real Madrid should have made it 3-0 in the 49th minute when Asensio released Isco in an advanced area, but the Spaniard could not find a route past Dmitrovic as the Eibar goalkeeper made another smart save.
Eibar continued to enjoy good possession as the match passed its hour mark, but the away side, who had most of their joy in wide positions, were not really threatening to breach Casilla's goal.
Ronaldo had a wonderful chance to get his name on the scoresheet in the 66th minute after being released by Isco, but the Portuguese was denied by Dmitrovic, and substitute Benzema fired the rebound over the crossbar.
Ronaldo then hit the side-netting from a Marcelo cross 10 minutes from time, but Real Madrid had their third in the 82nd minute when a wonderful passing move ended with Marcelo arrowing the ball into the bottom corner of the net.
Real Madrid's number seven continued to look for a goal in the latter stages, but Dmitrovic made another smart save in the 88th minute as the Portuguese was unable to add to his one league goal this season.