Ronaldo put Madrid ahead in the 34th minute after Luka Modric intercepted a loose ball from Eibar centre- back Aritz Arbilla and placed a flawless pass for the Portugal forward to control with his chest and fire in past Dmitrovic.
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.
Real Madrid is another four points back in third.
Taking into account the 30-year-old's return of 126 goals in 265 league outings across his near-decade at the Bernabeu, though, Zidane does not believe that he has to justify his decision to select the Frenchman.
Ronaldo now has 17 goals in his last 10 games in all competitions and his 18 league goal tally has him closing in on Lionel Messi who has 24.
Ronaldo subsequently punished that miss, meeting Dani Carvajal's right-wing cross with a powerful header that gave Dmitrovic no chance and sent Madrid back to the capital victorious.
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It would be a great career - 18 years in the National Football League .' I learned a lot and it's been such a great love for me. Gronk didn't play in the second half due to a concussion, but said he was feeling better when Gisele asked for an update.
"For me he's from another galaxy", Real coach Zidane said. His stats 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.
A sloppy pass out from the back by Anaitz Arbilla conceded possession to Modric, who quickly picked out Ronaldo.
The Spain worldwide returned to the pitch in the 78th minute, shortly before Cristiano Ronaldo struck the winning goal in a 2-1 win for Zinedine Zidane's side.
There was no embarrassment from Ramos after the game, as he joked about the incident on Instagram, posting a picture of him celebrating with Ronaldo.
"The important now is to keep picking up three points in every game".