Real Madrid opened their campaign with a draw while Deportivo, Gimnastic and Getafe all won.
Liga giants Real Madrid have been held by Villarreal in their league opener despite a number of new faces on show.
Along with coach Fabio Capello, the capital outfit had the likes of Fabio Cannavaro, Mahamadou Diarra and Ruud van Nistelrooy all on show.
However, it was a far from vintage display from Capello's charges as they struggled to break down an organised Villarreal outfit.
In the evening clash it finished all square as Athletic Bilbao drew 1-1 with Real Sociedad at Estadio San Mames.
The home side controversially took the lead when Aritz Aduritz netted from the penalty spot when it appeared it was he who handled in the box in the first place.
However, the visitors were not to be denied and they claimed a share of the spoils in the closing stages when Mikel Aranburu drilled home into the roof of the net.
Elsewhere, Gimnastic began life in Spain's top flight with a stunning 1-0 success over Espanyol thanks to Alejandro Campano's 51st minute strike.
Getafe kicked off the campaign with a 2-0 success over Osasuna thanks to second half goals from Fabio Celestini and Ruben Pulido.
Atletico Madrid completed a hat-trick of away wins as highly-rated striker Fernando Torres netted the only goal of the game to sink Racing Santander.
The visitors finished the contest with ten men following Giourkas Seitaridis' second half dismissal but Atletico held on for the points.
Recreativo de Huelva salvaged a late point at home to Real Mallorca thanks to Santiago Cazorla's injury time equaliser.
Juan Arango thought he had bagged all three points in the closing stages, but there was still time for Cazorla to grab a share of the spoils.
Deportivo La Coruna emerged victorious from a five-goal thriller at El Riazor on Sunday.
Real Zaragoza began the better of the sides with Diego Milito opening the scoring.
However, Juan Rodriguez's goal and Sergio's penalty ensured the home side entered half time in front.
Things went from bad to worse when Juanfran was dismissed and Depor moved 3-1 ahead when Javier Arizmandi found the back of the net.
The visitors never gave up and Ewerthon pulled one back but the 10-men were unable to muster a leveller.
Athletic Bilbao 1-1 Real Sociedad
Deportivo La Coruna 3-2 Real Zaragoza
Espanyol 0-1 Gimnastic
Osasuna 0-2 Getafe
Racing Santander 0-1 Atletico Madrid
Real Madrid 0-0 Villarreal
Recreativo Huelva 1-1 Mallorca