Ronaldo took his seasons league tally to 23, just hours after Lionel Messi had hit a fifth hat-trick of the season in Barcelonas 4-1 triumph at Malaga yesterday.
That put the Argentine star on 22 goals for the campaign as the champions temporarily cut the gap on their bitter rivals to two points.
On the day that Marca sports daily claimed coach Jose Mourinho had accused some Real stars of betraying him in the aftermath of the midweek Kings Cup defeat to Barca, things got worse for his side.
Fernando Llorente gave Athletic a shock lead after 12 minutes following an inch perfect pass from Javi Martinez and in an evenly-contested first half Oscar De Marcos was denied a second goal when keeper Iker Casillas blocked well.
But Real drew level with a well-worked team move which was finished by Marcelo.
Immediately after the restart Kaka was pulled back in the box by Ander Iturraspe and Ronaldo scored from the spot.
As Real continued to push forward they won a second penalty after 65 minutes when Mesut Ozil was felled by De Marcos, who received a red card, and Ronaldo converted from 12 yards.
Substitute Gonzalo Higuain then hit the post from a tight angle for a rampant Real before Jose Callejon, who also came off the bench, scored the fourth with five minutes to go.
Mourinho later denied he was concerned by whistles he received from sections of the Bernabeu crowd.
"This isnt a problem for me, it didnt happen when I was at Porto, Chelsea or Inter (Milan) but there is always a first time," he said.
"Is it difficult? We played and we won. Here they have whistled at Zidane, Ronaldo and Cristiano (Ronaldo), who has the Golden Boot, so why cant they whistle at me?" Mourinho asked.
"I will try and respond with my work. At Chelsea it would be difficult to accept the whistles but at a place where they whistle the best then who am I to say anything.”
"I wasnt born a Madrid fan. I am a professional, the directors, the legal representatives of the fans, employ me and I have a great relationship with them."
Earlier, Messi scored his 14th Barcelona hat-trick as the champions cruised to victory at Malaga.
Messi found the target in the 33rd, 50th and 80th minutes.
This was only Barcas fourth league victory on their travels and Messis goals also brought to an end a poor personal run as only one of his 19 goals going into the game had come away from home.
Barcelona coach Pep Guardiola left Carles Puyol, Cesc Fabregas and Xavi Hernandez on the bench with one eye on Wednesdays second leg cup clash with Real.
Still it was a sluggish first half from the Catalan side and Malaga had the better openings notably for Isco Alarcon, who had a shot well-saved by keeper Victor Valdes.
He was denied twice more by the shot-stopper with a header and a close range strike.
But Messi then headed home an Adriano cross to put the visitors ahead after 33 minutes.