Ramos left the field to go to the toilet after 73 minutes at the Ipurua Municipal Stadium, with the match delicately poised at 1-1.
With 50 minutes on the clock, Ramis headed home unchallenged from the resultant corner from Pedro Leon.
Ronaldo, who scored in the 2-1 win at PSG on Tuesday as Real Madrid moved into the Champions League quarter-finals, has now scored 13 goals in his last seven games.
The 33-year-old's tally for club and country this season stands at 35 goals in 37 appearances.
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Zinedine Zidane had insisted the success in Paris was now "forgotten" and his starting line-up suggested as much, with Karim Benzema the only key player rested. What he does, is always very positive for us; he knows he is going to score. He is a different player, a special player. "The statistics speak for themselves".
The win has now temporarily closed the gap between Real and their fierce rivals Atletico Madrid to four points as Zidane's side look to stay in touching distance of the top two.
Eibar appeared to target Madrid's full-backs and their crosses from both flanks continued to trouble, even if they often just missed the intended target.
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"It's true that after 15, nearly 20 days, Luka came in and played a great game", Zidane said.
Madrid had used all three subs already, one of which saw Raphael Varane replaced by Nacho after just 28 minutes.
A sloppy pass out from the back by Anaitz Arbilla conceded possession to Modric, who quickly picked out Ronaldo.
Eibar's leveller led to Real placing more emphasis on scoring a second and it soon became a game of attack versus defence as the hosts attempted to keep hold of a share of the spoils.
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And from the resulting corner, Ramis lost Sergio Ramos and headed beyond the helpless Navas to equalise.