Karim Benzema scored twice in the second half at Estadio Alfredo Di Stefano, lifting Madrid to a fourth straight victory in all competitions.
Zinedine Zidane's men joined Real Sociedad and Atletico Madrid on 26 points atop the table, but they struggled for large parts at home to Athletic.
Madrid played more than 75 minutes against 10 men following Raul Garcia's red card, but Toni Kroos' fine opener was cancelled out by Ander Capa.
But Benzema haunted Athletic once more to continue Madrid's winning run.
Big @Benzema with another brilliant header!