Karim Benzema of Real Madrid celebrates after scoring his side's second goal against Athletic Bilbao on Tuesday in Madrid. Photo: VCG

Real Madrid were made to toil by the 10 men of Athletic Bilbao but eventually won 3-1 on Tuesday thanks to two strikes from Karim Benzema to go level on points with La Liga leaders Real Sociedad.

Athletic forward Raul Garcia was sent off in the 13th minute for a second booking, but Real only managed to take the lead right at the end of the first half thanks to a low drive from Toni Kroos.

The Basque side continued to cope well with their numerical disadvantage into the second half and grabbed an equalizer through Ander Capa in the 52nd minute before Benzema managed to head the champions back in front in the 74th.

Athletic substitute Mikel Vesga then had a glorious chance to equalize in added time but was thwarted by an outstanding save from Thibaut Courtois and Benzema killed the game off by finishing on the counterattack immediately after.

A third consecutive league win took third-placed Real on to 26 points after 13 games, level with second-placed Atletico Madrid and leaders Real Sociedad but having played two games more than Atletico.

Athletic are 13th on 14 points.

Real had enjoyed a remarkable last week, beating Sevilla and Borussia Moenchengladbach before a comprehensive 2-0 win over local rivals Atletico to ease the pressure on coach Zinedine Zidane after a stuttering start to the campaign.

The Frenchman made only one change to the starting 11 that had beaten Atletico, bringing in Federico Valverde for the suspended Casemiro, and his side's heroic recent efforts seemed to have taken their toll in the early stages of the game.

"This was a very important victory and will help us to keep growing," said Madrid midfielder Valverde.

"They defended very well and were causing us a lot of danger on the counter but the coach corrected that at halftime."

Athletic, meanwhile, made an energetic and aggressive start and could have had a penalty when Inaki Williams was pushed over in the area by Dani Carvajal.

Moments later, they were down to 10 men after Garcia charged into a tackle on Kroos and was deservedly shown a second yellow card.

Madrid really struggled to take advantage but their quality eventually shone through.

"We stood our ground until the end, and Courtois won the game with that save before the third goal went in," said Athletic's Oscar de Marcos.

"We deserve more credit for the way we are competing but it's a real shame because everything is going against us lately.

"The red card was very early and conditioned the game a lot. It's very difficult to compete here with 10 players."