Real Madrid's first game of the year ended in a 2-0 defeat against Deportivo La Coruna, which began the game winless in nine matches.
Joan Capdevila and Cristian Hidalgo each scored to hand Madrid its second straight loss and extend its dismal record at Riazor stadium, where it hasn't won since the 1991-92 season.
Valencia notched its fourth straight victory and left Villarreal in 11th place, winless in four matches. Valencia forward Miguel Angel Angulo gave his team a 1-0 win over Villarreal which moved it into fifth place.
Villarreal dropped playmaker Juan Roman Riquelme for Matias Fernandez, the club's new signing from Colo Colo who was recently voted South American player of the year.
Fernandez made little impact in a first half dominated by the visitors although the Chilean struck the post with a drive from outside the area in the 68th minute.
Also on Sunday, it was: Real Betis 1, Celta Vigo 0; Espanyol 0, Recreativo Huelva 1; Levante 2, Racing Santander 0; and Mallorca 1, Athletic Bilbao 3.
Sevilla, which lost to Zaragoza 2-1 on Saturday, leads the league with 37 points. Barcelona is next with 35 points, followed by Madrid with 32, and Zaragoza and Valencia on 30 each.
Matches were preceded by somber music as a mark of respect for two Ecuadoreans who were killed on December 30 in a car bombing at Madrid airport. The attack was blamed on Basque separatist group Eta.