They found themselves ahead after 12 minutes when Benzema converted from outside the box and it was quickly two as Sergio Ramos thumped a header home from close range.
Benzema added his second and Madrid's third moments later, but Bilbao did gain a route back into the match just before the break when Ibai Gomez found the bottom corner.
Here, Sports Mole dissects the 90 minutes of action between the two La Liga rivals.
On target 18
On target 1
Was the result fair?
The short answer is yes. Madrid were stunning this evening, it is as simple as that. They started the match with such a quick tempo and deservedly opened up a three-goal lead before being pegged back before the interval. Their performance did not suffer, however, and they added two more goals late on. Bilbao will have no complaints, they just met a very good Madrid side tonight.
Real Madrid's performance
8/10. If Madrid play like this against Manchester City on Wednesday then the Premier League champions will have to go some to take something from the match. Benzema and Ozil were wonderful, while Luka Modric had his best night in a white shirt. They scored five and Cristiano Ronaldo was not among the scorers.
Athletic Bilbao's performance
6/10. Bilbao were not particularly bad this evening, they just met Madrid at the wrong time. They were handed a way back into the match late in the opening period, but never really threatened to pull their way back into it. Bilbao's season will not be shaped on results against the likes of Madrid, especially not when Jose Mourinho's side play like that.
Sports Mole's man of the match
Karim Benzema: The French striker has had his critics this season, but he was stunning tonight and his second goal was of the highest order.
Biggest gaffe of the match
Bilbao should have been awarded a penalty when Fabio Coentrao handled inside the penalty area early in the second period, but the referee waved play on and moments later Madrid were 4-1 ahead. It was poor from the linesman who was in close proximity.
Jose Teixeira had a fairly solid 90 minutes of action this evening. He went unnoticed for large periods of the match, which is always a good sign for a referee. However, he should have awarded Bilbao a penalty in the second period.
Real Madrid: Madrid face a crucial Champions League clash against Manchester City on Wednesday before returning to league action away to Real Betis next Saturday.
Athletic Bilbao: Bilbao are also in European action this week against Ironi Kiryat Shmona before hosting Deportivo La Coruna in the league next Sunday.