Harry Kane nets his first hat-trick of the season as Bayern hammer Holstein Kiel

Harry Kane scored his first hat-trick of the season as Bayern Munich routed promoted Holstein Kiel 6-1 to climb back to the top of the Bundesliga table.

Kane’s first-half double, coupled with Jamal Musiala’s opener and a Nicolai Remberg own goal, had Bayern 4-0 up by half-time at the Holstein Stadion, and substitute Michael Olise’s first goal for his new club and a late Kane penalty simply cemented a perfect start to the campaign despite substitute Armin Gigovic’s late consolation strike.

Champions Bayer Leverkusen responded to the loss of their 35-game unbeaten league run against RB Leipzig last time out with a resounding 4-1 win at Hoffenheim.

Victor Boniface’s double coupled with Martin Terrier’s strike and a Florian Wirtz penalty claimed the spoils as Mergim Berisha replied at the Rhein-Neckar Arena.

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Ermedin Demirovic scored twice as Stuttgart eased to a 3-1 win at Borussia Monchengladbach after Alassane Plea had cancelled out Deniz Undav’s opener for the visitors.

Junior Adamu scored twice inside three second-half minutes to fire Freiburg to a 2-1 victory over Bochum, who had taken the lead through Myron Boadu on the stroke of half-time.

Eintracht Frankfurt needed Omar Marmoush’s late penalty to win 2-1 at Wolfsburg after Ridle Baku had cancelled out his first-half opener, while RB Leipzig and Union Berlin finished goalless.

In LaLiga, Real Madrid needed second-half penalties from Vinicius Junior and Kylian Mbappe to see off a stubborn Real Sociedad 2-0 at the Reale Seguros Stadium.

Vinicius struck from the spot with 58 minutes gone after Sergio Gomez has been penalised for handball, and Mbappe followed suit 15 minutes from time following Jon Aramburu’s foul on Vinicius.

Ayoze Perez fired Villarreal to a 2-1 victory at 10-man Real Mallorca, who had Toni Lato sent off, to extend their unbeaten start to the new campaign after Raul Albiol’s own goal had dragged the hosts back into it following Logan Costa’s strike.

Javi Puado’s hat-trick, which was completed from the penalty spot, saw Espanyol beat Alaves 3-2 in a thriller.

Tomas Conechny levelled after Puado had given the hosts the lead, but the frontman had assured himself of the match ball by the time Nahuel Tenaglia scored the visitors’ second.

Jesus Navas fired 10-man Sevilla to a hard-fought 1-0 win over Getafe in which substitute Juanlu Sanchez picked up a late red card.

Christian Pulisic and Tammy Abraham both scored from the penalty spot as AC Milan beat promoted Venezia 4-0 to claim their first Serie A win of the campaign.

Skipper Theo Hernandez, Youssouf Fofana, Pulisic and Abraham all scored inside the opening 29 minutes on a night when the visitors had Hans Nicolussi Caviglia sent off for two bookable offences.

Empoli continued their unbeaten start to the season with a creditable 0-0 home draw with Juventus, although the point with which Bologna emerged from their trip to Serie A new boys Como was earned in more eventful fashion.

Cesc Fabregas’ men looked to be heading for their first win since promotion when Nicolo Casale’s own goal and Patrick Cutrone’s effort gave them a 2-0 lead, but substitutes Santiago Castro and Samuel Iling Junior snatched a 2-2 draw.

Ousmane Dembele came to Paris St Germain’s rescue as the Ligue 1 champions fought back to beat Brest 3-1 and resume their place at the top of the table.

The visitors took a shock 26th-minute lead through Romain Del Castillo’s penalty but Dembele headed them level before the break and then struck again seconds after Fabian Ruiz had put them in front during a second-half blitz.

Goals from Thilo Kehrer, Vanderson and Denis Zakaria eased Monaco to a 3-0 win at Auxerre, while Neal Maupay and Luis Henrique were on target as unbeaten Marseille saw off Nice 2-0 despite having Derek Cornelius sent off for a second bookable offence with 16 minutes remaining.

Meanwhile, Republic of Ireland striker Troy Parrott scored four times as AZ Alkmaar trounced Eredivisie rivals Heerenveen 9-1.

Parrott, who was an unused substitute in both of Ireland’s 2-0 Nations League defeats by England and Greece, scored his side’s second goal before the break and then added three more inside eight second-half minutes.