Cristiano Ronaldo netted twice for Los Blancos to secure a 2-1 victory and three LaLiga points to add to their tally.
Five minutes into the second half, Ivan Ramis drew level for Eibar with a great header off a corner by Pedro Leon.
With six minutes left, Ronaldo sent a bullet header beyond goalkeeper Marko Dmitrovic for his 13th goal in his last seven games in all competitions, sealing victory for Real.
His 33 goals this term means only Harry Kane (35) has scored more in all competitions than the Portugal global this season.
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"He's from another planet", Madrid manager Zinedine Zidane said after the match.
"With Gareth I have no problem, he's a fundamental player for us, very important, and he's going to play until the end of the season, like the rest". He is a different player, special. "The statistics speak for themselves".
After the intermission, and with a goal in their pocket, Real Madrid tried to slow the game's pace, but Eibar did not allow them to.
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"There are days when we do not do play so well".
"Luka was out for nearly three weeks, came back and played very well", he said.
Raphael Varane had to be replaced by Nacho after taking a bang to the head and, against the run of play, Real edged ahead in the 33rd minute. Ronaldo used his chest to control Modric's pass before scoring. He chested the ball down and slammed it in at the near post.
Sergio Ramos has played more than 550 games for Real Madrid, but apparently he's not above pooping his trousers in the middle of a game.
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Ronaldo seemed destined to restore their lead when Bale passed into the area just after the hour mark, but Dmitrovic produced a sensational save to deny him. They would soon prove costly misses. His whipped cross found the leaping Ronaldo and the Portugese made no mistake.