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Real soon began to threaten after Angel di Maria drove towards goal on 17 minutes, but the winger could not find the finish.
The home side eventually took the lead on 26 minutes when Karim Benzema found Isco in the area, and the Spaniard calmly rolled the ball into the bottom corner.
Benat Etxebarria almost found an equaliser for Bilbao on the half-hour mark but his strike missed the target.
Madrid grabbed a second just before half time through Cristiano Ronaldo, who headed home a Di Maria cross to extend his side's lead.
Bilbao made a positive start to the second half, with Iker Muniain causing problems down the wing for the Madrid defence.
Ronaldo came close again on 71 minutes from a free kick, although the goalkeeper got down well to make the save.
Isco then made it 3-0 two minutes later with a sweeping effort outside the area that left the goalkeeper with no chance.
Ibai Gomez grabbed a late consolation for the away side, picking up a loose ball and firing home on 80 minutes.