Real remain 15 points behind leaders Barcelona and four adrift of second-placed city rivals Atletico, who host Celta Vigo today.
Modric was excellent throughout, the Croatian providing a sublime pass with the outside of his foot for Ronaldo's opener. After Ronaldo gave his side a 1-0 lead in the 34th minute, Eibar did not switch off for a moment and made sure that the Madrid side did not do much damage to their game plan.
That was to be Eibar's last chance for the day as Madrid were more than happy to keep possession of the ball for the three minutes of added time, keeping the home side as far away from the ball as possible.
With clashes to come early next month against Atletico Madrid and then the Champions League quarter-final, an argument could have been made to rest the club legend yet again, for the third time in five league matches - preserving his premium match sharpness.
Ramos poked fun at himself after the game on social media, tweeting "nature calls" along with a picture of him and Ronaldo celebrating the goal.
"(Ronaldo) is from another galaxy", Madrid coach Zinedine Zidane said.
Ronaldo's bullet header from Dani Carvajal's cross in the 84th minute earned Madrid the three points.
French giants Paris Saint-Germain are set to undergo a meeting with their world record signing Neymar, as the Brazilian continues to draw links with Real Madrid. "He knows that he will score".
'The numbers speak for themselves and I'm just glad he is with us. Ronaldo used his chest to control Modric's pass before scoring.
Madrid defender Raphael Varane was substituted in the 26th after a blow to the head.
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.