Lionel Messi scored twice as Barcelona made the best start in the history of the Spanish league with a 5-1 win over Athletic Bilbao.
Real Madrid extended their dominance over the second place Atletico Madrid by easing to a 2-0 victory in La Liga.
Robin Van Persie scored the winning goal in the 34th minute as Manchester United defeated Reading 4-3.
Swansea set a big upset as the two goals by Michu helped them defeat Arsenal 2-0 at Emirates Stadium.
Marouane Fellaini put Everton in front at Manchester City but then conceded a penalty kick that allowed Carlos Tevez to clinch a 1-1 draw for City.
Rafa Benitez's winless start as Chelsea manager worsened as West Ham took advantage of Chelsea's weak defense, and came from behind to beat their London rival 3-1.
Liverpool recorded only its second win in seven Premier League matches by beating Southampton 1-0 from Daniel Agger's first-half goal.
Juventus provisionally extended their Serie A lead by beating 10-man Torino 3-0 in the Turin derby.