After securing a 5-2 aggregate victory over Paris Saint-Germain in the Champions League last 16 on Tuesday, Real swapped the Parc des Princes for the smallest ground in La Liga, with a capacity of just over 7,000.
With the score locked at 1-1 after Ivan Ramis cancelled out Cristiano Ronaldo's first-half opener, the Spain worldwide left the field in the 73rd minute.
A second goal would have led to Real being in full control of the contest but within six minutes of the restart, Eibar were back on level terms as Ramis sent a header into the net from 10 yards after meeting Leon's corner.
Before kick-off, Atletico Madrid and Barcelona had been the only two sides to leave Eibar with all three points since the end of October and Zinedine Zidane's side struggled to get to grips with their wingers during the early exchanges.
"(Ronaldo) is from another galaxy", Madrid coach Zinedine Zidane said.
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'He knows that he's going to score, he's very positive.
His double means Ronaldo has now scored in seven consecutive games and has a remarkable 13 goals overall in that period. His stats speak for themselves. But he was running really well, if not faster than normal, so something seemed fishy.
But for Ronaldo's clinical instincts in front of goal, that slip-up should have proved costly and Eibar deserved something from a match in which they poured their heart and soul into.
But a defensive error allowed Dani Carvajal to cross and Ronaldo headed in.
Rodrigo Moreno scored twice to give Valencia an important away victory that opened up an 11-point advantage over fifth-place Sevilla.