0338 GMT January 19, 2020
Ronaldo netted the opener against the run of play (34), finishing from 12 yards after being played through on goal by Luka Modric, skysports.com reported.
Eibar defender Ivan Ramis equalized with his third goal of the season, a header from a corner (50), but Ronaldo won it with six minutes remaining with a close-range header, his 17th goal in just 10 games.
The result means Real has now 57 points from 28 matches, while Eibar has 39 points from the same number of games.
The host started well as Real Madrid's defense struggled to settle, but the champion’s first chance resulted in a goal after 34 minutes Ronaldo flashed home in the box after being found by Modric's superb through ball with the outside of his boot.
It should have been 2-0 before the break, but Eibar goalkeeper Marko Dmitrovic did brilliantly to tip over Ronaldo's deflected effort from the edge of the box.
Eibar leveled five minutes after the break through Ramis, who got up above Sergio Ramos to power a header past Keylor Navas from Pedro Leon's corner.
Dmitrovic again denied Ronaldo after the hour-mark with a superb diving save to his right from 12 yards, before Bale glanced a header inches wide from the resulting corner.
Eibar then had two chances of its own; first Takashi Inui headed over the bar from six yards as the ball awkwardly bounced in front of him, before Kike struck wide from an angle with just Navas to beat after Joan Jordan's through ball.
But Ronaldo won it in the 84th minute, ghosting in-between the Eibar center-backs to power a header home from Dani Carvajal's clinical cross.