Ronaldo was then handed his marching orders for clashing with Carlos Gurpegi, as Madrid passed up the chance to move ahead of Barcelona and into second spot in the La Liga table.
Here, Sports Mole dissects the 90 minutes of action between the two Spanish rivals.
On target: 6
On target: 2
Was the result fair?
In truth, neither side deserved to leave with nothing this evening. Bilbao were the better team in the first period and perhaps should have taken a lead into the interval, but Los Blancos dominated proceedings for long periods of the second half. All things considered, neither manager will be too disappointed with a share of the spoils during a pulsating and dramatic evening at San Mames.
It is not too difficult to see why Bilbao have not been beaten on their own patch in La Liga this season. The Basque outfit draw energy from the incredible atmosphere inside the stadium, and that was indeed the case for much of the first period. They struggled to match Madrid's intensity in the early stages of the second half, but showed their character to respond after falling behind. There is no question that they look the favourites to secure a top-four finish and the chance to play Champions League football next season in the process.
Madrid were brilliant in the first 10 minutes, but did not get going again until the second period. When Jese opened the scoring, it looked to be another three points for Carlo Ancelotti's side, but they could not keep out an impressive Bilbao outfit. The capital outfit are still to hit top form this season, but have been dogged defensively in recent weeks, which will stand them in good stead for the remainder of the season. As it stands, they sit three points behind leaders Atletico Madrid.
Sports Mole's man of the match
Sergio Ramos: The Madrid centre-back has his critics, but it is difficult to argue against his performances in recent weeks. The Spanish international continued his impressive recent form this evening as he demonstrated all aspects of his game. He was his usual calm and composed self in possession, while he was aerially dominant against the aggressive and awkward Aritz Aduriz.
Ronaldo was foolish to raise his hands after exchanging words with Gurpegi deep in the second half, but the reaction from the Bilbao centre-back was extremely poor. The Portuguese did touch the face of the defender, but there was minimal contact. Quite why Gurpegi decided to throw himself to the ground remains a mystery.
There were a number of solid challenges in the first period, but Miguel Ayza was sensitive to the occasion and didn't produce a yellow card until the half-hour mark when he booked Xabi Alonso. Both sets of players continued to put pressure on the official in the second half, and he was perhaps forced into producing a red card for Ronaldo when a yellow perhaps would have sufficed. Overall, it was a difficult night for Ayza.
Bilbao: The Basque outfit will attempt to return to winning ways in La Liga when they travel to Celta Vigo next Monday.
Madrid: Los Blancos are in Copa del Rey semi-final action on Wednesday as they host capital rivals Atletico Madrid for the first leg.