Sergio Ramos and a Ruud van Nistelrooy brace had sealed the win for Madrid before Fernando Llorente hit a late consolation for the hosts.

A further strike from Guti cemented the win and ensured Fabio Capello's men remain within touching distance of second-placed Sevilla and league-leaders Barcelona.

The result also served to worsen Bilbao's relegation fears, leaving the Basque club in 16th position on 32 points and edging dangerously close to the relegation zone.

Madrid's first goal came after 15 minutes from defender Sergio Ramos. David Beckham delivered a trademark pin-point free-kick from the right wing which found Ramos lurking at the back post and he made no mistake with his header.

The visitors were controlling the tempo of the game and playing with a calmness which has been lacking at times this season.

They limited Bilbao to very few opportunities, Joseba Etxeberria enjoying the pick of them midway through the half, but the Spain international fired over from 12 yards.

Madrid recorded their second in the 34th minute through the more familiar goalscoring figure of Van Nistelrooy. This time it was Cicinho who provided the perfect cross and the former Manchester United marksman had little trouble in heading home from inside the six-yard box.

Robinho came close to increasing Madrid's advantage with a long-range attempt just before the break and Bilbao goalkeeper Daniel Aranzubia was more than a little relieved to see it fizz narrowly wide of the mark.

It took just four second-half minutes for Madrid to find their feet and re-establish their superiority.

And the third goal came via the same formula as the second, Cicinho again finding Van Nistelrooy from the right and the Dutchman converting emphatically, this time with a sweet, right-footed drive into the roof of the net.

The goal quashed any hopes the hosts had of turning the game around and their second-half chances were as few and far between as in the first.

Ander Murillo's 25-yard volley flew comfortably wide and served to sum up Bilbao's evening.

Andoni Iraola also tried his luck in the 65th minute but Real goalkeeper Iker Casillas was able to punch to safety, and minutes later he made another top save from Aritz Aduriz's goalbound volley.

But the home side were to get a consolation with 10 minutes to go, Llorente heading home Fran Yeste's free-kick to give the San Mames crowd something to cheer about.

But it was head-in-hands time once again just two minutes later, when Raul found Guti in space and the midfielder finished with a cheeky lob from inside the area, to hammer the final nail in Bilbao's coffin.

The win leaves Madrid on 60 points, two behind Barcelona and one behind Sevilla with just four games remaining.