But a defensive error allowed Dani Carvajal to cross and Ronaldo headed in.
However, Eibar managed to level matters five minutes into the second half when Iván Ramis powered a header into the bottom corner after meeting a cross from Leon. "He knows he's going to score, he's unique and special".
Victory means Zinedine Zidane's side have won eight of their last nine matches in all competitions, but still trail LaLiga leaders Barcelona, who have a game in hand, by 12 points.
Eventually Madrid appeared to exert a degree of control and Ronaldo - following a moment of Luka Modric inspiration - opened the scoring in the 34th minute, continuing his brilliant recent form. Tiny Eibar are in contention for a European place next season and made the better start to the game, with Zidane admitting his side struggled in the opening stages. "This is a very hard ground to come to and they know how to play here".
Sergio Ramos thundered a shot wide after good defending from Ramis, while Ronaldo was denied his second goal by a fantastic save from Dmitrovic and Modric fired straight at the Serbian as Los Blancos improved just before the break.
Bale had a chance to restore Real's lead in the 63rd minute but his header sailed inches wide of the upright.
Later on Saturday, Valencia moved back to within a point of Real and all but ended Sevilla´s hopes of finishing in the top four by beating Los Rojiblancos 2-0.