Sergio Ramos 73rd minutes goal from the spot was all Real Madrid needed to record their seventh consecutive victory as they go seven points clear of tittle challengers Barcelona.
Real Madrid were presented with the chance to go seven points clear at the top of La Liga, with Barcelona set to face Villarreal later.
It was a hard-fought contest similar to that of their last game against Getafe. Real Madrid saw few genuine goalscoring chances. Karim Benzema and Rodrygo both wasted good opportunities in the first half at a sunshine-drenched San Mames courtesy of Asensio crosses.
The decisive moment of the game came in the second half when Madrid were awarded a penalty kick for a foul by Dani Garcia on Marcelo inside the box, spotted after a VAR check. Ramos stepped up to convert his fifth goal in his last seven games and his 10th La Liga goal of the season as a whole.
Marco Asensio started for the first time this season after a long time injury which initially ruled him out of the season if not for the covid 19 pandemic, he saw an early free kick saved by Athletic keeper Unai Simon and he also created two clear-caught chances that almost led to a goal.
Real Madrid were far from their best at San Mames, their defence was tested in the first half but Thibaut Courtois gave a good account of himself with two fantastic saves, this was his 17th clean sheets in laliga this season, he as arguably been the best goalkeeper in Spain this year.
Real Madrid will be back in action on Friday night as they host Deportivo Alaves amid their title charge, before visiting Granada the following Monday.
Athletic, meanwhile, will take on Sevilla in Bilbao on Thursday night ahead of their trip to Levante next weekend