Bottom side Deportivo La Coruna stunned fourth-placed Malaga, while Levante, Valencia and Sevilla also prevailed in La Liga on Saturday.
Deportivo, under the guidance of new manager Domingos Paciencia, defied the odds with a 1-0 victory against Malaga.
Former Braga and Sporting boss Paciencia, who replaced the sacked Jose Luis Oltra at the start of the week, was delighted as Pizzi scored the only goal of the match in the 57th minute.
Deportivo climbed to 19th on the table, equal on points with 16th-placed Celta de Vigo and league safety.
Malaga, who defeated Real Madrid 3-2 last time out, missed the opportunity to move above the champions to third place.
Meanwhile, 10-man Athletic Club failed to hold on for a point following the dismissal of young defender Aymeric Laporte and went down to Levante 3-1.
Athletic Club took the lead through Aduriz in the sixth minute before Christian Lell levelled proceedings 20 minutes later.
Laporte was sent off in the 43rd minute and Levante took advantage soon after when Iborra headed home two minutes later.
Nabil El-Zhar's 69th-minute goal put the result beyond doubt, handing Athletic Club, who reached the finals of King's Cup and Europa League last season, their ninth loss of the season.
Elsewhere, Valencia came from behind to defeat 10-man Granada 2-1 away from home and Emir Spahic's 83rd-minute goal handed Sevilla a 1-0 win over Osasuna, who slipped to bottom place.