• Inter’s late win over Juventus extends Serie A lead

• Real Madrid 4-1 Real Sociedad; Lens top of Ligue 1

Harry Kane scored twice in the first half as Bayern Munich cruised to a 3-0 win at Werder Bremen, restoring their six-point lead in the Bundesliga. Borussia Dortmund’s 4-0 win over Mainz on Friday put them within three points of the league leaders but Bayern responded.

Bayern were in control from start to finish in Bremen, with Leon Goretzka joining the England captain on the scoresheet in the 70th minute. Kane now has 26 goals in 22 Bundesliga games this season and 41 in all competitions, 13 of those from the penalty spot.

• Bellingham out for month with hamstring injury

• PSG return to top of Ligue 1 despite Hakimi red card

Kylian Mbappé stayed calm to roll home a 100th-minute penalty and secure for Real Madrid a 2-1 win over nine-man Rayo Vallecano on Sunday in a spicy La Liga derby. Los Blancos’ victory cut Barcelona’s lead back to one point at the top of the table after the Spanish champions beat Elche on Saturday.

Vinícius Júnior scored early on for Madrid after Jude Bellingham limped off with an apparent hamstring injury. Jorge de Frutos pulled Rayo level early in the second half, prompting visible anger from the Madrid fans at their team. Frustration was averted when Mbappé netted from the spot following Pathé Ciss’s red card at the death. Rayo also had Pep Chavarría sent off before the final whistle.

• Roma have £21.6m option to buy forward

• Winger Ta Bi arrives from Maccabi Netanya

Donyell Malen has left Aston Villa after only a year with the club to join Roma. The Serie A side have signed Malen on loan with an option to buy.

The loan fee is reported to be £1.7m, with the fee should the deal be made permanent understood to be £21.6m. That will only come into force should certain conditions are met.

• David’s failed Panenka costs Juventus against Lecce

• Chelsea target Rosenior’s Strasbourg draw at Nice

The Barcelona manager Hansi Flick hailed Joan García as one of the best goalkeepers in the world after the former Espanyol player delivered a decisive performance against his old club in the Catalan derby on Saturday.

García was instrumental in Barcelona’s 2-0 victory, producing a series of outstanding saves, with the league leaders extending their lead at the top of the La Liga standings to seven points.

The Argentinian captain has his critics but is the leader and inspiration behind a team finding their feet again

Leave it to a 20-year-old, with three Serie A starts under his belt, to provide a most perceptive analysis of the Italian top flight as we head into a new year. “The most difficult thing to do in this game,” said Francesco Pio Esposito on Sunday night, “is to stick the ball in the net.”

He was speaking in praise of his Inter teammate, Lautaro Martínez, whom he set up for the decisive goal in a 1-0 win away to Atalanta. Pio Esposito had barely entered as a second-half substitute when he was gifted possession by an opponent, Berat Djimsiti. Instead of taking the chance on himself, he froze the last defender and released Lautaro to score with a side-footed through-ball.

• Forward scores only goal of the game in 65th minute

• Milan had gone top earlier in day by beating Verona 3-0

Lautaro Martínez scored to give Inter an important 1-0 win at Atalanta on Sunday, sending his side into the new year at the top of Serie A. Inter lead a tightly contested league table on 36 points, one clear of Milan and two ahead of Napoli.

Marcus Thuram appeared to have put Inter into the lead just before the interval, but the goal was ruled out after an offside by Martínez in the build-up. Atalanta felt a similar sense of frustration soon after the restart when Nicola Zalewski broke through one-on-one with Yann Sommer, only for the Inter goalkeeper to produce a spectacular leg save.

• Barcelona head into new year on top of La Liga

• Kane scores again in Bayern’s 4-0 rout of Heidenheim

Barcelona enjoyed a composed 2-0 La Liga victory at Villarreal on Sunday thanks to goals from Raphinha and Lamine Yamal in a match that tilted firmly in the visitors’ favour when the hosts were reduced to 10 men just before the break.

It took only 12 minutes for Barcelona to take the lead from the penalty spot after Santi Comesana blocked Raphinha with his back as the winger tried to break through and the Brazilian calmly converted the spot-kick.

Manchester City conquer the Bernabéu, Liverpool survive without Mohamed Salah and Atalanta find Chelsea’s flaws

• To say that Pep Guardiola and Real Madrid have history is to put it mildly. At Barcelona, Guardiola grew up amid an obsessive enmity on both sides, one deepened by his term as the Catalan club’s coach. They are highly familiar with Manchester City, too. City met Madrid for the fifth season in succession on Wednesday. Despite Madrid’s recent struggles under Xabi Alonso, winning at the Santiago Bernabéu is a huge result, a deserved win where City might have been out of sight by half-time. Rodrygo scored his habitual goal against City but one of Guardiola’s new generation in Nico O’Reilly equalised before a controversial penalty award, converted by Erling Haaland, decided the game. A player linked with a move to Madrid sometime in the distant future celebrated with a smirk; Jude Bellingham’s attempt to distract by trying to yank Haaland’s ponytail did not work. After the selection misstep that led to defeat to Bayer Leverkusen, Guardiola got it right in Madrid to leave a lifelong rival in flux. In acknowledging an opponent wracked by injury and infighting had made for an easier task than usual, high standards came to the fore. “I’ve been here [at the Bernabéu] many times in the last five years and we have played much better than today and not won,” Guardiola said. He talks – and his team plays – like he has his mojo back.

There were no answers to Chelsea’s search for consistency here. Instead they supplied more evidence that they lack the resilience for a Champions League tilt that may now have to be tackled the hard way. This damaging late defeat completed a grim week on the road and had implications for the longer-term picture. They are staring down the barrel of a February playoff that could stretch Enzo Maresca’s side, active almost year-round, to the very limit.

Atalanta twice punished weak defending and, crucially, preyed on their opponents’ inability to overcome setbacks. It is a problem Chelsea cannot quite shrug off and, at this level, such recidivism comes at a cost. When Charles De Ketelaere, the game’s outstanding player, blasted in a deflected winner after being invited to take aim they could hardly claim not to have been warned.

• Forward says he is ‘building confidence’ with Maresca

• Manager praises Atalanta before Champions League tie

Alejandro Garnacho has said that he has no regrets about the manner of his departure from Manchester United, and that it was a straightforward decision to “take a step forward” by ­joining Chelsea last summer.

Garnacho has had a steady, rather than sparkling, first few months since he joined Chelsea in August. His relationship with Ruben Amorim had collapsed by the end of his five‑year stint at United and he was banished from the squad in pre‑season. Amorim felt he had failed to follow tactical instructions and, before the transfer was completed, said he sensed Garnacho wanted “a different thing with different leadership”.

• Mbappé scores twice and Camavinga once in 3-0 win

• Kane scores and gives away penalty as Bayern progress

Kylian Mbappé scored twice as Real Madrid defeated Athletic Bilbao 3-0 to end a three-match winless run in La Liga.

Mbappé’s France teammate Eduardo Camavinga also scored as Real moved back within a point of Barcelona, who defeated Atlético Madrid 3-1 on Tuesday.