Ronaldo put the European champions ahead in the 34th minute following a lovely pass from Luka Modric.
Eibar responded well to going a goal behind, though, and restored parity just minutes into the second half, with Ivan Ramis losing Sergio Ramos from a corner kick to head past the helpless Keylor Navas.
Ronaldo's bullet header from Dani Carvajal's cross in the 84th minute earned Madrid the three points.
Heading closer towards the business end of the season and with Madrid qualifying for the quarter finals of the Champions League, Zidane and the Madrid fans will be hoping to have Varane back sooner rather than later for what could be Real's only chance at silverware this season.
"This is a very hard ground to come to and they know how to play here". This year, Ronaldo scored 17 goals before January, a number he's already equaled in 2018 and we're not even halfway through March.
Victory means Zinedine Zidane's side have won eight of their last nine matches in all competitions, but still trail LaLiga leaders Barcelona, who have a game in hand, by 12 points.
"For me, he's from another galaxy", Real coach Zidane said.
It happens to the best of them, just ask Gary Lineker.
After the win, Real sits in the third spot with 57 points, four points behind second-placed Atletico Madrid, who are scheduled to take on Celta Vigo on Sunday.
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.
Sergio Ramos simply couldn't hold out for full time when his stomach began urging him to visit the bathroom late on in Real Madrid's La Liga clash with Eibar.