Real Madrid stayed on top in La Liga, while Juventus took an early lead as Serie A got under way.
Celtic leapfrogged Motherwell into second place in the Scottish Premier League to keep leaders and Old Firm rivals Rangers under pressure.
Ajax knocked FC Twente off the top spot in the Eredivisie, Montpellier remain in pole position in Ligue 1 and Bayern Munich retained the lead in style in the Bundesliga.
Karim Benzema scored a double as Real Madrid retained their spot at the top of La Liga with a 4-2 home victory over Getafe on Saturday, while reigning champions Barcelona were pegged to a 2-2 draw at Real Sociedad thanks to Antoine Griezmann's equaliser for the hosts.
Valencia remained in second place after Roberto Soldado's goal sealed a 1-0 home win over Atletico Madrid, while Villarreal and Sevilla shared the spoils after drawing 2-2 in Saturday's other game.
On Sunday Real Betis moved up the table into third after a Ruben Castro strike secured victory at home to Real Mallorca.
Osasuna and Espanyol were winners elsewhere, while the games between Racing Santander and Levante and Rayo Vallecano and Real Zaragoza ended in goalless draws.
Scottish Premier League
Ally McCoist's Rangers held onto the top spot in the Scottish Premier League after beating Dundee United 1-0. Kyle Lafferty scored the only goal at Tannadice in a game which saw Terrors striker Johnny Russell sent off in the first half.
But Old Firm rivals Celtic cut the Gers' lead to just a point after thrashing Motherwell 4-0 at Parkhead, with James Forrest bagging a brace for the Hoops.
Kilmarnock edged a 3-2 win over Dunfermline Athletic while Inverness Caledonian Thistle were held to a 1-1 draw by Hearts after a late Stephen Elliot goal.
St Mirren and St Johnstone took a point apiece after a goalless draw in Paisley and Sunday's only game ended with the same scoreline after rock-bottom Hibernian were held at home by Aberdeen.
Juventus sit top after the first round of fixtures having demolished Parma 4-1 on Sunday, while Cagliari, Udinese and Fiorentina also secured wins.
Inter Milan were edged out 4-3 at Palermo thanks partly to a brace from Fabrizio Miccoli for the home side and the three remaining games of the weekend ended in draws.
Bayern Munich retained pole position in the Bundesliga after an emphatic 7-0 thumping of SC Freiburg, during which Mario Gomez landed four goals.
Second-placed Werder Bremen remain in hot pursuit thanks to their 2-0 home triumph over Hamburg, while Stuttgart, Hoffenheim, Borussia Monchengladbach and Hertha Berlin were also winners.
On-loan midfielder Joe Cole made his Lille debut on Saturday to help the French side to a 3-1 triumph at St Etienne, while AC Ajaccio, Toulouse and Lyon were also winners.
Marseille suffered a 1-0 defeat at home to Rennes after substitute Jires Kembo Ekoko scored a late goal and Sochaux drew 1-1 with Lorient.
Saturday's final game between Bordeaux and Evian TG ended in a 0-0 stalemate, while Sunday's action saw Montpellier retain the top spot as they beat Nice 1-0, Paris St Germain see off Brest by the same scoreline and Nancy draw at home to Auxerre.
Ajax remain unbeaten this season and top of the Eredivisie following their 3-2 win at Heracles Almelo on Saturday after FC Twente suffered their first defeat of the campaign to Roda JC.
AZ Alkmaar kept the heat on Ajax with a 4-0 thrashing of Vitesse, while De Graafschap and RKC Waaljwijk were Saturday's other victors.
In Sunday's action PSV Eindhoven were frustrated by lowly VVV Venlo in a 3-3 draw and Feyenoord moved into fourth place with a 3-1 win over NAC Breda.
Heerenveen and FC Utrecht were also winners over Groningen and Excelsior respectively.
Best of the rest
CSKA Moscow have edged ahead of Zenit St Petersburg by a point at the top of the Russian Premier League, while Porto are early leaders by two points in the Portuguese standings.
Helsingsborgs continue to plough ahead in the Swedish Allsvenskan after extending their lead at the top to seven points, while Molde are still on top in Norway and HJK Helsinki now boast a 14-point cushion in Finland.
Gent are top in Belgium but only on goal difference, with Cercle Brugge level on points, while the Turkish Super Lig is yet to get under way.