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It took just 12 minutes for the hosts to open the scoring, as Karim brought down a high ball to fire into the net.
Just three minutes later it was 3-0 and game over for the hosts, Benzema getting his second with a delicious bending effort into the corner.
Bilbao managed a goal back just before half-time, with Ibai Gomez finishing well from close range.
Any nerves that goal might have created were eliminated on 56 minutes, Ozil finishing off a counter-attack to give Madrid a 4-1 win.
It was 5-1 on 72 minutes through Sami Khedira, who finished low.
Despite continued Real dominance there were to be no more goals as the match ended 5-1.