Harry Kane scored his ninth goal of the season to help Bayern Munich cruise to a 3-1 win over Mainz and climb to third in the Bundesliga. Kane headed home from close range in the 16th minute after Kingsley Coman had given Bayern the lead following good work from Leroy Sané. The hosts looked to have little to offer in terms of attacking threat but pulled a goal back in the 43rd minute when Anthony Caci found too much space on the left and rifled home. Mainz had a golden chance to level through Stefan Bell but his shot sailed narrowly wide in the 57th. That proved costly as two minutes later Bayern made it 3-1 thanks to Leon Goretzka’s low drive from the edge of the box. Bayern trail Bayer Leverkusen by two points. Leverkusen remain top thanks to a battling 2-1 win at Wolfsburg. Jeremie Frimpong and Alejandro Grimaldo scored either side of an equaliser from Maxence Lacroix to secure a seventh win in eight league matches. Bundesliga top-scorer Serhou Guirassy scored again in Stuttgart’s 3-0 win at Union Berlin. Guirassy took his tally to 14 goals in eight games by taking Stuttgart’s first chance in the 16th minute but had to go off with a hamstring injury in the 30th. Silas Katompa Mvumpa doubled the lead on a counterattack in the 81st, before Deniz Undav completed the scoring with a header in the 88th. It was Stuttgart’s sixth straight victory and stretched Union’s losing run across all competitions to eight games. Loïs Openda scored twice as RB Leipzig won 3-1 at promoted Darmstadt, Eintracht Frankfurt won 3-1 at Hoffenheim while Freiburg defeated Bochum 2-1. A late header from captain Dani Carvajal secured Real Madrid a 1-1 draw at Sevilla in La Liga. Real had two early efforts disallowed and fell behind after an own goal by defender David Alaba in the 74th minute before Carvajal’s towering close-range header levelled the scores four minutes later. Sevilla confirmed that a home fan was removed from the ground and reported to the authorities for “xenophobic and racist behaviour”. A statement from the club said: “Sevilla condemns any racist and xenophobic behaviour, even in isolation, as is the case, and shows its willingness and collaboration with the authorities to eradicate these attitudes, which do not represent a fanbase like Sevilla’s.” Atlético Madrid’s Antoine Griezmann scored a hat-trick to earn his side a 3-0 win at struggling Celta Vigo, who played most of the La Liga match with 10 men after goalkeeper Iván Villar was sent off early in the first half. The French striker opened the scoring from the spot in the 29th minute after Villar was shown a straight red for a last-man foul inside the penalty area on Álvaro Morata. The visitors then wasted several chances to extend their lead before Griezmann finally struck from inside the box in the 64th minute. He then guaranteed the win six minutes later with a tap-in from close range. Atlético, who have a game in hand, are second in the table, three points behind leaders Real Madrid. Former Liverpool manager Rafa Benítez’s Celta are in the relegation zone with six points from 10 games. Real Sociedad won 1-0 against Mallorca thanks to a second-half goal from Brais Méndez while Getafe drew 1-1 with Real Betis. Goals from Marcus Thuram, Lautaro Martínez and a penalty by Hakan Calhanoglu gave Internazionale a 3-0 win at Torino to send them back to the top of Serie A. First-half goals by Felipe Anderson and Luis Alberto earned Lazio a comfortable 2-0 win at Sassuolo, securing Maurizio Sarri’s side their first back-to-back Serie A wins in the campaign. The Rome side jumped six places to seventh in the table on 13 points. Sassuolo are now 13th with 10 points. Khvicha Kvaratskhelia struck twice after Matteo Politano had opened the scoring as Napoli won 3-1 at Verona. Kylian Mbappé was in top form as Paris Saint-Germain secured a 3-0 home victory against Strasbourg, scoring one goal and creating another. Mbappé put PSG ahead after 10 minutes with a penalty after Gonçalo Ramos was brought down. Carlos Soler extended the lead shortly after the half-hour mark after a cutback from Mbappé, while Fabian Ruiz secured the three points in the 77th minute, deftly manoeuvring past two defenders inside the box before finding the back of the net. Nice moved top of Ligue 1 on Saturday courtesy of a late header by Evann Guessand that secured a 1-0 home victory against Olympique Marseille. Nice are top of the table with 19 points, two ahead of third-placed Monaco who play Metz on Sunday. Paris Saint-Germain are second on 18 points.