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.
With Barcelona in action against Malaga later on Saturday (11:45pm UAE time) and Atletico Madrid playing host to Celta Vigo on Sunday (7:15pm), Real closed the gap on their city rivals to four points but are still 12 points off Blaugrana.
Five minutes into the second half, Ivan Ramis drew level for Eibar with a great header off a corner by Pedro Leon.
Ronaldo has scored in his last seven appearances in all competitions, and Zidane said: "He is from another galaxy".
Before kick-off, Atletico Madrid and Barcelona had been the only two sides to leave Eibar with all three points since the end of October and Zinedine Zidane's side struggled to get to grips with their wingers during the early exchanges.
"He knows that he's going to score, he's very positive".
The early loss of Raphael Varane with a head injury upset Real's back four but still, seasoned campaigner Nacho came off the bench.
A sloppy pass out from the back by Anaitz Arbilla conceded possession to Modric, who quickly picked out Ronaldo.
It didn't matter that Real Madrid's game at Eibar was delicately poised at 1-1 in the second half; captain Sergio Ramos could wait no longer.
Ronaldo should have restored the advantage but failed to convert an excellent Bale cross and from the resulting corner, Bale flashed a glancing header just wide of the post.
Lucas Vazquez and Karim Benzema replaced Isco and Toni Kroos as Zidane looked to raise the tempo and find a second goal. They would soon prove costly misses.
Ronaldo struck a fine goal in the 84th minute making it 2-1 for his side. His whipped cross found the leaping Ronaldo and the Portugese made no mistake.