Los Blancos responded to Barcelona's victory over Malaga to secure a first title in four years, ending Pep Guardiola's domestic dominance with an emphatic win at San Mames
Pep Guardiola's side had easily dispatched of Malaga earlier on Wednesday, leaving Los Blancos requiring a win, and they duly obliged, despite Cristiano Ronaldo's early penalty miss. Gonzalo Higuain's superb strike gave Jose Mourinho's side the lead after 16 minutes, and the visitors doubled their advantage soon after through Mesut Ozil.
Ronaldo completed the scoring in simplistic fashion soon after the break, with Javi Martinez's sending off allowing Madrid to cruise to victory.
The championship-chasing visitors started in determined fashion, as Gorka Iraizoz was forced to rush off his line to deny Higuain following Xabi Alonso's through ball inside the opening minute.
As the Basques began to settle, Javi Martinez needlessly raised his hand in the penalty area, leaving Ronaldo with the opportunity to open the scoring from the spot. The Portugal international attempted to gently lift the ball down the centre of the goal, but Iraizoz was quick to react, turning the ball over the bar.
Los Blancos' endeavour was finally rewarded, however, and in breathtaking fashion. A swift counterattack
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The Basques responded positively, and could easily have been awarded a penalty when Markel Susaeta saw his shot blocked by Khedira's outstretched arm, only for his appeals to be waved away.
Xabi Alonso then underlined his array of passing when, with the outside of his right boot, he found Ronaldo, whose equally perfect low cross found Ozil at the far post to double Madrid's lead.
The half ended in frantic fashion as both sides were denied by the woodwork. Mikel San Jose's deflected strike hammered back off the bar following Iker Casillas' flying save from Inigo Perez, and in response Ozil's effort clipped the frame of the goal on the way behind.
Madrid's energetic start to the match was replicated after the break as Higuain's magical run past four Athletic defenders, ended with his shot being deflected for a corner kick. It was 3-0 from the resulting set piece when Alonso delivered the ball into the six yard box and Ronaldo gleefully headed home unchallenged.
With the Basque beginning to look drained in what was their 59th match of the season, Real looked to extend their lead. Alonso's majestic reverse pass gave Jose Callejon a sight of goal but the winger's first touch took him away from goal and he was unable to generate enough pace on his shot to beat Iraizoz.
Bilbao continued to offer a threat to Casillas' goal and were denied by the crossbar for a second time when Oscar de Marcos thrashed an effort off the frame of the goal.
Athletic were thenreduced to 10 men after Javi Martinez, booked for handling in the first half in giving away the penalty, was sent off for the same offence.
The game's end prompted a pitch invasion of the small travelling contingent of Madrid fans as they celebrated their first league title in four years.
Real Madrid will look to complete a season of records, which has seen Jose Mourinho win his fourth different domestic league following successes with Porto, Chelsea and Inter, and his side could end the campaign with 100 points if they triumph in their two remaining games.