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Lamine Yamal stood out for Barcelona in a bad-tempered and spectacular 5-2 win at Real Betis on Saturday that maintained the visitors' perfect start to La Liga before a Champions League showdown with Paris Saint-Germain.
PSG also won, coming from behind with substitute Ousmane Dembélé missing a penalty before later scoring in a 3-1 victory at Strasbourg in the French league.
Under-fire Manchester City stayed perfect in the Premier League, while Bayern Munich hit six goals against visiting Leipzig in the Bundesliga.
Yamal scored arguably the day's finest goal across all the European leagues, but was later booked after clashing with a rival player, who was sent off.
The 19-year-old Ballon d'Or contender scored the opening goal when he eluded Facundo Bernal by rolling his foot over the ball just outside the penalty area, from where he sent it sailing inside the far post in the 10th minute. He justifiably looked very pleased with himself.
Valentín Gómez headed Betis' reply, Rodri restored Barcelona's lead, and Giovani Lo Celso had an equalizer before the break ruled out through VAR. Betis coach Manuel Pellegrini was booked for his protests.
After the break, Yamal set up Gabriel Jesus for Barça's third goal, only for Abde Ezzalzouli to reply for Betis two minutes later, when Yamal and Bernal clashed off the ball.
It appeared Bernal pushed Yamal, who barged back into Bernal and the two tussled. Bernal moved his head toward Yamal, touching his forehead. Yamal immediately dropped to the ground and rolled on the field, clutching his forehead. Bernal was shown a red card, Yamal a yellow.
Eric Garcia got Barcelona's fourth goal shortly afterward, before Dani Olmo completed the scoring late.
Barcelona, which has won each of its nine league games, next faces two-time defending champion PSG away in the Champions League on Tuesday.
Álex Baena scored in the 89th minute for Atlético Madrid to beat Espanyol 1-0 away to stretch his team's winning run to six games across all competitions. The result increased the pressure on Espanyol coach Manolo González after a fifth defeat from nine games for the club owned by American Alan Pace.
PSG rallied against Strasbourg after United States midfielder Gio Reyna had broken the deadlock in the 17th minute with a low shot that took a slight deflection past Matvey Safonov.
PSG coach Luis Enrique evidently had the upcoming clash with Barcelona in mind as he started with Dembélé, Désiré Doué, Vitinha, Nuno Mendes and Achraf Hakimi all on the bench.
They were on the field by the time Dembélé fired the spot kick wide in the 72nd after Pape Demba Diop was penalized for hand ball.
But Ukraine defender Illya Zabarnyi finally equalized five minutes later, Dembélé popped up with what seemed the winner in the 85th, and Doué made sure in stoppage time.
Pedro Neto scored early and late in the second half to lead Chelsea to a 2-0 win at Everton in a Premier League match marred by a serious-looking head injury to Chelsea goalkeeper Emi Martínez.
Chelsea handed Everton a first loss of the season after seven rounds, keeping a first clean sheet in nine months in the process.
Scandal-hit Manchester City maintained its perfect start with a 3-2 home win over Ipswich. Playing in front of fans waving inflatable bananas, City became only the third team to open a Premier League season with seven straight wins by beating Ipswich 3-2 at home.
Liverpool rallied to win 2-1 at Brentford.
Harry Kane took his tally to 102 goals in 100 Bundesliga games as Bayern Munich rebounded from an uncharacteristic 2-game winless run with a 6-1 rout of visiting Leipzig.
Luis Díaz scored a hat trick for Bayern, which next faces Arsenal in the Champions League in Munich on Wednesday.
Borussia Dortmund won all its games before the international break and has not won any since after being held 0-0 at Union Berlin for its second straight Bundesliga draw. It comes after Wednesday's Champions League loss at Bodø/Glimt.
Dortmund had greater concerns about Konstantinos Karetsas, however. The 18-year-old Greece winger went on as a substitute only to be helped off eight minutes later with what looked like a right ankle injury. There was no immediate update from the club.
Promoted Elversberg won 4-3 at home against Augsburg, Hamburger SV held on for a 1-0 win over Stuttgart, Mainz won at promoted Schalke 1-0 and Werder Bremen fought back to draw 2-2 against promoted Paderborn.
Napoli slumped to another defeat with Akor Adams' strike giving Venezia a 1-0 win for its first Serie A points of the season.
Kevin De Bruyne saw his penalty saved by Venezia goalkeeper Filip Stanković as Massimiliano Allegri's team suffered its second straight loss — after its Champions League defeat to Villarreal — and a third loss from seven games in the Italian league.
Adams chased Simon Sohm's hopeful punt forward and capitalized on a mistake from Napoli defender Amir Rrahmani to win the ball and shoot past goalkeeper Alex Meret with the aid of a deflection from Rrahmani's desperate challenge just after the break.
De Bruyne should have scored after Matias Moreno brought down Rasmus Højlund, but Stanković saved the Belgian's spot kick in the 68th.
It gave new Venezia coach Davide Nicola a winning start after replacing Giovanni Stroppa on Wednesday.
Inter Milan won 3-1 at Bologna.
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