Barcelona made it back-to-back wins in LaLiga as goals from Lamine Yamal and Robert Lewandowski secured a 2-1 victory over Athletic Bilbao.
Hansi Flick's men joined Celta Vigo as the only sides so far to take maximum points from their first two matches, with teenager Yamal opening the scoring midway through the first half.
Oihan Sancet converted a first-half penalty for Celta, but Lewandowski's drilled low finish with 15 minutes left proved to be the winner.
Osasuna winger Ruben Garcia's solitary second-half strike sank Real Mallorca 1-0 and lifted his side into the top five, while Takefusa Kubo's late effort sealed Real Sociedad a 1-0 win at Espanyol and Getafe drew 0-0 with Rayo Vallecano.
Jamie Gittens struck twice as Borussia Dortmund made a winning start in the Bundesliga with a 2-0 home win against Eintracht Frankfurt.
The 20-year-old Londoner, who joined Dortmund from Manchester City in 2020, broke the deadlock with a fine individual effort midway through the second half and added another just before full-time.
Freiburg are early table-toppers as Lukas Kubler scored twice in a 3-1 home win against Stuttgart, who had taken an early lead through Ermedin Demirovic. Ritsu Roan was also on target for the home side.
Antonio Nusa struck the only goal as Leipzig held on to beat Bochum 1-0 after the late dismissal of Willi Orban, while Holstein Kiel's first-ever Bundesliga match - they were in the third tier in 2017 - ended in a 3-2 defeat at Hoffenheim.
Werder Bremen were held 2-2 at Augsburg and Mainz drew 1-1 at home against Union Berlin.
In Serie A, reigning champions Inter Milan kick-started the defence of their title with their first win of the season, 2-0 at home against Lecce.
Matteo Darmian (above) headed Inter, who were held by Genoa in their opening match, into an early lead and Hakan Calhanoglu converted a second-half penalty.
City rivals AC Milan slipped to a surprise 2-1 defeat at Parma and remain winless after their first two matches.
Christian Pulisic cancelled out Dennis Man's second-minute opener for the home side before Matteo Cancellieri fired home a second-half winner.
Genoa are in second place after following up last week's home draw against Inter with a 1-0 win at Monza thanks to Andrea Pinamonti's first-half header, while Udinese sit fourth after a 2-1 defeat of Lazio.
In Ligue 1, Lille made it two wins from two by beating Angers 2-0 at home to move second in the table behind Paris St Germain, thanks to Thomas Meunier's first-half strike and Mohamed Bayo's stoppage-time effort.
Monaco sit third after back-to-back victories as Eliesse Ben Seghir and Lamine Camara scored second-half goals in a 2-0 win at Lyon, who are bottom, while Le Havre won by the same score at winless St Etienne.
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