Madrid made the breakthrough after only seven minutes when Radamel Falcao powered in an unstoppable left-footed drive from inside the area after shrugging off the attention of a couple of Bilbao defenders.
Marcelo Bielsa's side appeared unflustered by the early setback and they could have drawn themselves level when Fernando Llorente put his header just wide of the post.
The striker should have done better minutes later, but he could only slice his close-range volley wide while under pressure from two defenders.
Bilbao again pressed as Iker Munain's shot was parried away by Thibaut Courtois before Madrid doubled their lead at the break as Falcao turned cleverly in the box before he fired into the net.
Athletic were better after the interval and pushed forward in search of a way back into the match.
Adrian's curled effort flew narrowly wide, while Ibai Gomez's fierce volley only just cleared Thibaut Courtois's crossbar.
Bilbao then bombarded the Madrid goal as Markel Susaeta's deflected shot almost crept in. Susaeta was then denied by Courtois as the ball bounced around in the area.
Meanwhile, Falcao was denied a hat-trick at the other end when his shot clipped the outside of the post.
As Bilbao pushed further upfield, Madrid put the match to bed thanks to Diego's composed finish into the far corner with five minutes to play.