But Ronaldo proved the difference again, the 33-year-old taking his tally for the season to 35 goals in 37 appearances.
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.
And the visitors were ahead after 34 minutes when Modric intercepted a pass from Anaitz Arbilla before playing a sumptuous through-ball for Ronaldo to drill home at the near post.
Former Wigan defender Ivan Ramis headed in an equaliser for Eibar and it looked like they would secure a point.
Just before the break, Ronaldo forced a stunning stop out of Dmitrovic after his 20-yard strike was deflected on goal, with Sergio Ramos sent a free header wide of the post from no more than 10 yards out.
Real responded immediately with a good passing move resulting in Modric laying off for Ronaldo but his effort flew over the crossbar, before the Croatian dragged another shot wide of the post after a driving run.
The home side continued to control the early stages of the fixture and in the 19th minute, Kike Garcia and Takashi Inui linked up before Garcia saw his 25-yard curler tipped behind for a corner by Keylor Navas. They would soon prove costly misses.
Sevilla trailed Valencia by eight points before kick-off but that gap was stretched to 11 after two goals from Rodrigo Moreno sealed a comfortable victory.
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