Real Madrid have only won three of their last nine league away games (D4 L2), failing to score in three them.
Modric was excellent throughout, the Croatian providing a sublime pass with the outside of his foot for Ronaldo's opener.
Eibar were only promoted to the top flight for the first time in 2014, so Ronaldo has less experience playing against them than he does the majority of other clubs in La Liga at the moment. "He knows he is going to score". We didn't play a good game technically, but we were up against a great adversary.More news: Media 'Feasts' on Vulnerable, Possibly Drunk Former Trump Aide
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Los Blancos were forced into a first-half change as Nacho replaced Raphael Varane, who sustained a knock to the head in the 28th minute. He chested the ball down and slammed it in at the near post.
Why did Ramos leave the field halway through the second half? Sergio Ramos lost his man at a corner and Ramis nodded in from six yards.
Real were ragged early on as Takashi Inui, Kike Garcia and Joan Jordan all went close to giving Eibar the lead.
Luck appeared to have deserted Madrid after it wasted several chances, with Ronaldo among those guilty, but the Ballon d'Or holder produced an emphatic late header with his 17th goal in 10 games, moving it to within four points of Atletico, which faces Celta Vigo on Monday (NZDT). His whipped cross found the leaping Ronaldo and he made no mistake.
Real responded immediately with a good passing move resulting in Modric laying off for Ronaldo but his effort flew over the crossbar, before the Croatia worldwide dragged another shot wide of the post after a driving run.
Ronaldo scored his 32nd and 33rd goals in all competitions this campaign to move one ahead of his Barcelona rival.