The world's most expensive player has endured a frustrating start to the season, being booed and whistled by home and away fans, with his anxiety to score a goal clear for all to see.
His wayward shots, exaggerated complaints to the referee and occasional wild challenge had fans at the Anoeta howling until he struck a fierce free-kick which ballooned off the wall and past a stranded Claudio Bravo after 75 minutes.
"Cristiano is Cristiano, we are not going to change him," Real director general Jorge Valdano told Spanish television.
"He has a personality that enables him to be one of the best players in the world, we accept it and understand it as one of his strengths."
Argentina winger Angel di Maria had put the visitors in front at the start of the second half only for Raul Tamudo to level soon after.
Despite dominating possession it was the hosts who created the clearer chances until Di Maria scored a great solo effort in the 51st minute, curling a shot into the top corner.
The lead only lasted 11 minutes, Tamudo arriving unmarked at the far post to bundle in a free-kick and Real needed Ronaldo's strike, which deflected off Pepe's back in the wall, to restore the lead.
FURIOUS REACTION
Real Sociedad refused to lie down and near the end an error from Sergio Ramos led to Iker Casillas having to save on his line, prompting a furious reaction from his coach Jose Mourinho who jumped from his seat and hurled a plastic bottle into the dugout in digust.
"They were stronger in the first half, we were in the second. I think a draw would have been the fairest result," Mourinho told reporters.
Earlier, financially-troubled Real Mallorca recorded their first win of the campaign beating Osasuna 2-0 at home.
Gonzalo Castro set them on their way from the penalty spot after 25 minutes and Jonathan de Guzman ran the length of the pitch to secure the result in time added on.
The islanders finished fifth last season to qualify for the Europa League but were barred from entering the competition by UEFA after going into voluntary administration.
Athletic Bilbao fought back from two down to draw 2-2 at Sporting Gijon with goals from Carlos Gurpegi and Spain striker Fernando Llorente, while Espanyol overcame Almeria 1-0.
