Real Madrid recorded 20 goal attempts compared to only seven created by the visitors, who held their turf heroically to go home to San Sebastian with a point thanks to a string of saves by goalkeeper Alex Remiro.
Real Madrid lost ground in the LaLiga title race as they were held to a goalless draw at home to Real Sociedad.
The result left Madrid five points adrift of leaders FC Barcelona, who won at Girona on Saturday (Jan 28) and three points clear of third-placed Sociedad.
Brazil winger Vinicius Junior had the pick of Madrid's chances with three good opportunities. However, goalkeeper Alex Remiro excelled for the visitors with a string of fine saves to frustrate the hosts.
Meanwhile, Real's city rivals Atletico sit fourth in the table after Saul Niguez scored the only goal after coming on as substitute at Osasuna.
