Real remain 15 points behind leaders Barcelona and four adrift of second-placed city rivals Atletico, who host Celta Vigo today.
Eibar tied the score in the 50th minute when defender Ivan Ramis headed in a corner kick past Keylor Navas.
With Real chasing a victor, Ramos conspicuously went missing from the visitors' back four with 73 minutes played and the score finely poised at 1-1.
Zidane´s own future appears more secure following Real´s triumph in Paris, which pushes the club one step closer to an unprecedented third consecutive Champions League success.
The fact that PSG got knocked out of the Champions League has made things worse and PSG hope to convince him into staying by holding a meeting with him in Brazil soon enough.
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.
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Apart from the two well-taken goals, Ronaldo also stunned the watching crowd with a stunning improvisation while on the counter-attack.
"For me he's from another galaxy", Real coach Zidane said.
'He knows that he's going to score, he's very positive.
'The numbers speak for themselves and I'm just glad he is with us.
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.
In the 84th minute, Pedro Leon gave away possession too easily, allowing Modric to feed Daniel Carvajal out wide.
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.