Barcelona kept up their strong start to the season with a 2-0 victory at Getafe, while Real Madrid beat Espanyol 3-0.
Barcelona beat Sporting Gijon 3-0 in their opening Primera Liga match a fortnight ago but they were made to work harder by Getafe.
They could not break the deadlock in the first half and the stalemate continued until the 66th minute, when Zlatan Ibrahimovic stroked the ball home from close range.
Lionel Messi then headed home an Ibrahimovic cross on 80 minutes after a swift counter-attack to seal the win.
Real Madrid also claimed their second straight win with an emphatic success on the road against Espanyol.
Esteban Granero latched onto a pass from Kaka in the 39th minute to put Real ahead, while Guti made it 2-0 with a neat finish on 78 minutes.
Cristiano Ronaldo had started the match on the substitutes' bench but he came on to score a third in the 90th minute.
Atletico Madrid and Racing Santander picked up their first points of the new campaign after playing out a 1-1 draw at Vicente Calderon.
Jurado fired Atletico ahead in the 43rd minute before Oscar Serrado equalised for Racing on the stroke of half-time.
Sevilla got their campaign up and running courtesy of a 4-1 victory against Real Zaragoza in the late game of the day.
Abdoulay Konko set Sevilla on their way to three points with the opening goal after just eight minutes, although Javier Arizmendi soon drew Zaragoza level (19).
Luis Fabiano restored Sevilla's advantage on the stroke of half-time and Zaragoza never threatened a comeback in the second period.
Diego Perotti gave Sevilla a two-goal cushion in the 57th minute and Fabiano struck again with three minutes remaining.
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