The capital club's victory was their 14th in a row in all competitions and keeps Real top of the Liga standings for another week.
James Rodriguez opened the scoring midway through the first half to put Real on their way to a 36th Liga victory under Carlo Ancelotti in his 50th game in charge.
Eibar coach Gaizka Garitano had labelled Cristiano Ronaldo "unstoppable" before the game and that proved true as the Portugal captain doubled the advantage - scoring in the 11th consecutive Liga game in the process.
Real controlled things nicely in the second half with Isco replacing the injured Luka Modric in the midfield and bringing a similar calm as the Croatia star.
Karim Benzema scored for the fifth league game in a row and Ronaldo netted a late penalty to take his Liga tally for the season to 20 and add gloss to Real's dominant performance.
The European champions' focus now turns to guaranteeing top spot in their UEFA Champions League group, which they can do with a point against Basel in midweek.
Gareth Bale saw a fierce free-kick tipped into the air and onto the crossbar by Xabi Irureta as the visitors quickly regained their stride after a fortnight away.
The early pressure told in the 23rd minute, although Real were perhaps fortunate to not see Benzema flagged offside as he tried to flick Ronaldo's cross home - the Portuguese recovering the ball to clip into the path of Rodriguez to nod past Xabi.
Sergio Ramos was denied by Xabi from four yards and Bale lashed a half-volley wide after smart work from Ronaldo in a deeper area.
But the Eibar defence again fell asleep as Dani Carvajal burst up the right flank and squared for Ronaldo, who scuffed home from eight yards.
Real's incessant pressure continued after the interval with Xabi called into action again by Ramos before Isco was just off-target after a flowing move involving Benzema, Rodriguez and Ronaldo.
A third did arrive with 20 minutes to go as Marcelo and Rodriguez showed grit and determination to keep the ball in on the left-hand flank and Benzema profited from their work, hammering into the top corner from the Colombian's pass.
Ronaldo converted from 12 yards after his free-kick had been handled in the wall by Raul Albentosa and Real have now scored at least four goals in six of their last eight domestic fixtures.