Jose Mourinho's men were not at their most convincing, but did enough to collect the points through goals from Marcelo, Callejon, and a Ronaldo double from the spot
Fernando Llorente had given the visitors an early lead, but Marcelo restored parity with a fine goal, and two penalties from Cristiano Ronaldo plus a further strike from Jose Callejon added gloss to the scoreline.
With Barca collecting a confident 4-1 victory at Malaga earlier on Sunday, Madrid were searching for the win to regain the advantage on their rivals. Jose Mourinho made a number of changes to the side that lost in the Copa del Rey Clasico on Wednesday; Esteban Granero was handed a rare start, while Raphael Varane was given the nod in central defence due to the absence of Pepe.
The Basque visitors had, however, been in excellent form of late, and set about taking the game to the home side from the off. Indeed, it was no surprise when they took an early lead courtesy of Llorente.
A sweeping move saw Ander Herrera feed Javi Martinez, who had burst from his post in central defence to support the attack. His sublime cross from the right was met crisply on the volley by Llorente, leaving Iker Casillas with absolutely no chance.
The Bernabeu audience was not impressed, but Madrid continued to be subdued. Iker Muniain found space on the edge of the area, and his low effort could only be parried by Casillas into the path of Oscar De Marcos, but the wide player scuffed his close-range effort wide of the target.
Madrid then briefly came to life, long enough to level the scorelines. A neat set of exchanges between Marcelo and Ronaldo led to the Brazilian bursting into the area, and when faced with Gorka Iraizoz, composed himself suitably to curl into the net from 12 yards.
But the inevitable comeback from the hosts failed to transpire in the first half, and Bilbao should have entered the break in front. Llorente, who had finished so confidently earlier, this time skewed his shot wide of goal when one-on-one with Casillas.
However, normal service was resumed just 25 seconds into the second period. A lovely dummy from Kaka allowed Ronaldo to return the ball to the Brazilian, and Ander Iturraspe was caught wrong side. He dragged Kaka to the ground, and Ronaldo lashed the resulting penalty into the top corner in emphatic fashion.
Athletic's first half display was rendered irrelevant when Madrid sewed up the points on 66 minutes. Mesut Ozil burst through on goal, only to have his legs sweeped from under him by De Marcos. The referee gave the Bilbao man his marching orders, and Ronaldo once again finished with aplomb from the spot to make the score 3-1.
Jose Mourinho's side were far from at their best for long spells of the match, but now with a man advantage and having beaten Bilbao 5-1 in their last two clashes at the Bernabeu, they set about attempting to record a similar scoreline.
Gonzalo Higuain replaced Karim Benzema, and immediately smashed in a volley that Iraizoz did brilliantly to parry to safety. The he found space on the left and drillled in a low shot that cannoned back off the post.
But the honour of the fourth goal would fall to substitute Callejon. A sliderule through pass from Higuain sent the former Espanyol wide player through, and he slipped his shot across Iraizoz and into the far corner.
There was to be no more scoring, and Madrid move five clear at the top of the table, while Bilbao's bid for Champions League football next season has taken a dent.