Malaga used a first-half goal barrage to beat Zaragoza 5-3 in the Spanish league on Sunday, while Giuseppe Rossi scored twice as Villarreal cruised to a 4-0 win over Espanyol.
Malaga scored all of its goals in the first 34 minutes, including two goals each from Fernando Fernandez and Juan Miguel "Juanmi" Jimenez before Quincy Owusu made it 5-0 for the visitors.
Edmilson, Marco Perez and Ander Herrera led the fightback for Zaragoza, whose defense was in disarray in the first half. Malaga, meanwhile, rebounded from an opening day defeat to Valencia.
Like Malaga, Villarreal also recovered from defeat with its first victory of the season at El Madrigal stadium.
Italy striker Rossi opened the scoring in the 24th minute after collecting a pass from Borja Valero, who made it 2-0 eight minutes later.
Rossi slotted home a penalty in the 55th before Brazil striker Nilmar completed the rout in the 78th. Espanyol finished with 10 men after Francisco Javier Chica was red carded for scything down Jefferson Montero with five minutes to play.
Villarreal had started the season with a 1-0 defeat to Real Sociedad, which plays Almeria on Monday.
Elsewehere, Deportivo La Coruna held Sevilla to a 0-0 draw while Jaime Gavilan scored twice in Getafe's 4-1 win over Levante, and Sporting Gijon beat Mallorca 2-0.
Gavilan headed Getafe ahead after five minutes and Adrian Colunga doubled the advantage six minutes later from a one-on-one with goalkeeper Gustavo Munua.
Rafael Jorda struck a rising shot past goalkeeper Oscar Ustari for Levante in the 48th but Gavilan and Javier Arizmendi both scored in injury time to secure three points for the team from the Madrid suburbs.
In Gijon, Alberto Botia scored with a right-footed shot from inside the area in the 48th minute before Diego Castro's late penalty sealed victory for Sporting.
On Saturday, promoted Hercules stunned Spanish champion Barcelona 2-0 at the Camp Nou, while Real Madrid handed coach Jose Mourinho his first victory in charge of the Spanish giant with a 1-0 win over Osasuna. Both Madrid and Sevilla have four points.
Atletico Madrid beat Athletic Bilbao 2-1 to stay top of the standings with six points, just ahead of Valencia on goal difference after the Mediterranean coast club beat Racing Santander 1-0.
