After returning from a groin injury Isco started ahead of Toni Kroos, as Real also preferred Ferland Mendy, Marcelo, Lucas Vazquez and Marco Asensio from the win over Celta Vigo.
Real seemed to have gone ahead inside five minutes through the head of Karim Benzema following a floating delivery from Marcelo, but the Frenchman was flagged for offside.
Los Blancos were close to the breakthrough again right before the midway stage as Asensio curled a free-kick from a tight angle against the crossbar.
Eibar began to push forward close to the final stages of the first half and should've gone ahead from a speculative shot by Alejandro Pozo, but the attacker fashioned wide.
It was a missed opportunity that were duly punished by Real with Asensio picking up a ball from Carlos Casemiro to ran into the box before getting the better of goalkeeper Marko Dmitrovic.
Madrid looked to grab a second seven minutes from halftime through a smart attempt from a promising area by Asensio, but had Dmitrovic equal to the task.
The chances didn't stop coming Madrid's way soon before the latter stages as Benzema nodded a floating delivery from Vazquez well over the reach of Dmitrovic.
Los Blancos did eventually double their lead 73 minutes in when Benzema found space in the middle of the area to head home a cross from Vinicius Junior.
Eibar hoped to claim a consolation as Madrid attempted more goals, however 2-0 was the final score in the Spanish capital.