Los Blancos are now just three points ahead of Sevilla, who hold a match in hand.
LaLiga leaders Real Madrid saw their winning run come to an end after being held to a goalless draw by Villarreal at the Bernabeu.
Carlo Ancelotti’s side, who had thrashed Mallorca 6-1 on Wednesday night, are now just three points ahead of Sevilla who have a match in hand.
Thibaut Courtois made a smart save from Arnaut Danjuma before the break, while Karim Benzema was denied by Geronimo Rulli.
Earlier, Victor Laguardia’s early goal proved enough to give Alaves an unexpected 1-0 home win over Atletico Madrid, who suffered a first defeat of the campaign.
Alaves had lost their opening five games, but went in front after just four minutes through Laguardia’s header, who cleared a shot off the line during the second half to help secure all three points.
Youssef En-Nesyri’s early strike and a late goal from Rafa Mir helped Sevilla beat Espanyol 2-0 at the Estadio Ramon Sanchez Pizjuan.
Sevilla midfielder Thomas Delaney was sent off for two cautions in as many minutes during the second half.
Substitute Marcos Andre struck deep into stoppage time to grab 10-man Valencia a 1-1 draw at home against Athletic Bilbao.
Inigo Martinez broke the deadlock with 20 minutes left, and after Maxi Gomez saw red late on, it looked like no way back for Los Che.
However, with five of the seven additional minutes up, Andre drilled the ball home from close range for his first goal since his summer transfer from Valladolid.