Eibar dominated the opening 30 minutes before a wonderful pass from Luka Modric unlocked the home defence for Ronaldo to chest down and drill in from 12 yards.
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.
Ramos went off on minute 73 before Ronaldo had scored his second goal to give Real Madrid all three points in a 2-1 win.
After a slow start to the season, Ronaldo has netted 13 goals in his last seven appearances to take his total to 33 in 34 games this campaign. What he does, is always very positive for us; he knows he is going to score. He's a different and special player. His figures speak for themselves.
After the intermission, and with a goal in their pocket, Real Madrid tried to slow the game's pace, but Eibar did not allow them to.
Real still have a mountain to climb if they are to topple LaLiga leaders Barcelona, but that has not stopped the Frenchman from believing his side can retain their title.
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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.
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.
Zidane added: 'He's from another galaxy.
Ramos celebrates in the Champions League.
Isco and Kroos made way for Karim Benzema and Lucas Vazquez with 19 minutes left but Eibar had two golden chances to score a second.
Raphael Varane was forced to come off after a clash of heads during Real Madrid's La Liga clash with Eibar on Saturday.