Meanwhile, Gary Neville registered his first La Liga win as Valencia boss at the 10th attempt as they came from behind to beat Espanyol 2-1.
Ronaldo's early opener was cancelled out by Javi Eraso before a two-goal burst just before half-time from James Rodriguez and Toni Kroos put Madrid in control.
Real were reduced to 10 men late on as Raphael Varane received a red card, but Ronaldo made sure of the points before Gorka Elustondo grabbed a consolation in stoppage time.
Zidane 'proud' despite dent in Madrid title hopes
Barca have two games in hand on Madrid and face Celta Vigo in the first of those on Sunday.
Ronaldo had been much criticised for his poor performance as Madrid struggled past Granada last weekend.
Yet, back on home soil, he was back on top form as he turned inside from Karim Benzema's pass and smashed home his 31st goal of the season.
"The press are here to opine on whether Ronaldo plays well or badly, if he is finished, but today he has showed he is bloody brilliant," added Zidane.
Suarez, Messi hat-tricks hit Neville's Valencia for seven
However, Athletic reacted well to going behind in a hugely entertaining first half with chances flowing at either end.
The visitors were level on 10 minutes when Varane's errant backpass was only parried by Keylor Navas into the path of Eraso to slot home.
Navas then had to produce a brilliant save to parry Aritz Aduriz's powerful downward header and Aduriz came close again on the half-hour when his deflected shot came back off the crossbar.
However, the Basques were made to pay for their profligacy as Madrid showed their firepower with two goals in eight minutes before half-time.
Madrid players prefer Zidane to Benitez, says Ronaldo
Rodriguez regained the lead with a trademark drive into the bottom corner from outside the box for just his fifth goal of the season.
Kroos then put the game beyond Athletic as he received Ronaldo's pass just inside the area and saw his shot flick off Aymeric Laporte on its way past Iraizoz.
Madrid had to see out the final seven minutes with 10 men as Varane saw a second yellow card for leading with his elbow in an aerial clash with Aduriz.
Yet, even with a man less, Ronaldo got his second of the afternoon to move ahead of Luis Suarez as La Liga's top goalscorer by controlling Lucas Vazquez's cross before firing home from close range.
Athletic did eventually get the second goal their performance deserved in stoppage time when Elustondo rounded off the scoring from Oscar de Marcos's cross.
Valencia's first league win since November eases their relegation fears and the growing pressure on Neville's job.
"I'm happy with it, but it's just one small step forward. There is a big job still to do," said Neville.
"Relief is probably a good word (to describe it)."
The former Manchester United captain made the bold decision to recall goalkeeper Diego Alves for the first time in nine months after suffering cruciate ligament damage.
That decision paid dividends early on as the Brazilian made a brilliant reaction save to deny Felipe Caicedo before Mamadou Sylla inexplicably headed the rebound wide.
However, Alves was caught flatfooted for the opening goal seven minutes after half-time as Oscar Duarte flew in unmarked to head home Burgui's corner.
Alves made amends moments later with an incredible double save to deny Duarte and then Pape Diop.
Neville sent on Alvaro Negredo in search of an equaliser and, unlike in recent games when the former Spanish international has missed key chances, he came up with the goods as his deflected shot after a terrific run by Joao Cancelo trickled in 20 minutes from time.
And the game was turned on its head six minutes later as Sofiane Feghouli's cross from the right was powerfully met by Denis Cheryshev at the back post for his first Valencia goal.
Villarreal stretched their lead over Sevilla in fourth to 11 points thanks to Roberto Soldado's solitary goal in a 1-0 win over Malaga.
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