Athletic Bilbao have stunned Real Madrid 1-0 at the San Mames.
Real lacked their usual intensity and attacking flair, above all in the first half, and drop points for the second match running, following last weekend's 1-1 draw with Villarreal.
Bilbao won thanks to a first-half header by Aritz Aduriz.
They will surrender top spot to archrivals Barcelona if the Catalans beat Rayo Vallecano at home on Sunday.
Real coach Carlo Ancelotti said: "As always, I have to take a lot of the blame. There are some managers who disassociate themselves from their team if they do not play well. This is my team, they are not playing well and in this regard I am entirely responsible.
"I am not going to give in because the truth is that the league is going to get more difficult, but it is not over yet and we are going to fight to fix the situation quickly. We can look for a solution with the quality we have."