Ronaldo opened scoring with a fine finish from Luka Modric's pass.
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.
Eibar equalized in the 50th when defender Ivan Ramis broke free of Sergio Ramos to head home a corner kick by Pedro Leon.
As Real Madrid are on the verge of letting Karim Benzema and Gareth Bale leave the club.
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Diario AS reported this week that Barca's rivals Real Madrid have already told Neymar's father, who also serves as his manager, that they are willing to meet PSG's asking price of €400m.
And so off he went to find a bathroom, spending minutes 73-78 off the pitch before returning to witness Cristiano Ronaldo head the winning goal.
Real Madrid's next La Liga test comes at home to Pablo Machín's impressive Girona, while Eibar travel to Levante. "You can't give Madrid even half a chance because they will take full advantage of it".
Ronaldo and Neymar talk after a Champions League match.
Madrid remained third, 12 points behind leader Barcelona which visits Malaga later Saturday.
Paris Saint-Germain rocked the football world in the summer when they splashed £198 million to make Neymar the most expensive player in history.