The Portugal forward took his league tally for the season to 31 goals, netting in his eighth successive game in all competitions, and set up Gonzalo Higuain for Real's third.
Coach Jose Mourinho has said Real's title defence is effectively over but fielded a near full-strength side at San Mames as they moved on to 68 points, 13 short of leaders Barcelona with seven games left to play.
A weakened Barcelona side had earlier cruised to a 3-0 win at struggling Real Zaragoza thanks to two Cristian Tello goals.
Ronaldo stroked a free kick over the wall and into the top corner after only two minutes in Bilbao, but it sparked a strong response from the hosts who forced Diego Lopez into two fingertip saves before half-time.
Angel Di Maria had hit the bar in the first half and the temperature was rising as tackles flew in thick and fast.
Ronaldo was at the centre of much of the attention and reacted by outjumping his marker to thump Xabi Alonso's free kick past Gorka Iraizoz in the 68th minute.
Higuain was played into the space in the area by Ronaldo soon after, and the Argentine settled the match with low shot into the far corner.
Aitor Karanka praised Cristiano Ronaldo’s performance, brushing off fears of the Portuguese picking up an injury.
“Cristiano was limited in his play and had to endure many things,” Karanka responded post-game.
“And no, we have not substituted him for fear of injury. Not at all.
“Football is for men and even more in San Mames. Cristiano had the match he had and scored twice
“Athletic's players did what they needed to do. Cristiano did well in a tough atmosphere and has once again shown the type of player he is.
“He did what he had to do and scored two goals that won us the match.
“The reception towards him? Those who know him know how he is. There are ways of being that some people like more than others.
“He is dedicated to playing and scoring goals, that is what he does, and that is what he benefits from and that is that.”
It is the last occasion that Madrid play Athletic at San Mames, with the Basques moving to the new San Mames for next season.
“Clearly it is always special to come here and even more when you know it is the last time.
“These matches and these atmospheres give this stadium the history that it has and those of us that have played here know that and know it’s special.”
- Sports & Recreation
- Cristiano Ronaldo
- Real Zaragoza
- San Mames
- Gonzalo Higuain