Robert Lewandowski scored twice as Bayern Munich opened up a four-point lead at the top of the Bundesliga with a 3-2 win at second-placed Borussia Dortmund on Saturday.

Julian Brandt and Erling Haaland scored Dortmund's goals at Signal Iduna Park, but Lewandowski netted and converted the winning penalty, either side of a Kingsley Coman goal.

Dortmund coach Marco Rose was shown a red card for arguing with the referee after a Mats Hummels handball led to Lewandowski converting the key spot-kick 12 minutes from time. Lewandowski got a yellow card.

"In the first half, we should have led by more and in terms of how we played, I'm not sure we deserved to win," said Bayern forward Thomas Mueller. "But in terms of fighting, we were there."

This was Bayern's seventh straight win over Dortmund, including five Bundesliga victories and two German Super Cup triumphs.

Chelsea paid a heavy price for a 3-2 defeat at West Ham United as first Liverpool, then Manchester City, leapfrogged them in the Premier League title race on Saturday, with City ending the day on top for the first time this season.

Thomas Tuchel's Chelsea began the day with a narrow lead and twice went in front at the London Stadium, only to be stunned by a late goal from substitute defender Arthur Masuaku.

It looked as though Liverpool had let Chelsea off the hook as their later clash at Wolverhampton Wanderers went into stoppage time still goalless.

But Divock Origi, making his 100th appearance as a Liverpool substitute, latched on to a Mohamed Salah pass to smash a winner past Wolves keeper Jose Sa in the 94th minute.

Manchester City outclassed Watford in a 3-1 victory at Vicarage Road, with Raheem Sterling paving the way before Bernardo Silva struck twice in the day's late kickoff.

It meant Chelsea slipped to third place with 33 points from 15 games, one point behind Liverpool and two behind Manchester City. West Ham have 27 points.

"We are not good enough in the details at the moment," Tuchel told reporters. "We do too many big mistakes."

Georginio Wijnaldum's injury-time equalizer allowed Paris Saint-Germain to snatch a 1-1 draw away to Lens in Ligue 1 on Saturday in a match that confirmed Lionel Messi's difficulties adapting to the physical nature of French football.

Messi was floored by a strong tackle, and some PSG players stopped playing in the build-up to Seko Fofana's goal, which gave Lens a 62nd-minute lead in northern France.

It looked as if that would be enough for Lens to claim a victory which would have been a just reward for an outstanding performance that delighted the crowd of close to 37,000.

However, PSG equalized in the second minute of injury time as Kylian Mbappe crossed for fellow substitute Wijnaldum to head home.

It is the second draw in as many matches for the Qatar-owned club, who extend their lead at the top of Ligue 1 to 13 points from Marseille, beaten 2-1 at home by Brest earlier on Saturday.

It was a PSG side missing Neymar, who is out with an ankle injury and not expected to return before mid-January, while their nine-goal top scorer Mbappe was rested at kick-off before coming on to help save the day.

Messi still has just one goal from nine Ligue 1 appearances, and he struggled to make his presence felt against an impressive Lens side who lie fifth in the table.

On Saturday, Real Madrid secured a 2-0 win against Real Sociedad after traveling north to San Sebastian as they moved eight points clear at the top of La Liga.

With striker Karim Benzema forced off after 17 minutes with a hamstring injury, it was once again Vinicius Jr. who stood out by scoring his 10th goal of the season and driving the home side's defense crazy with his boldness and audacity.

Real's man of the hour, 21-year-old "Vini," has been one of the standout players in Europe during this campaign and is two goals behind Benzema at the top of La Liga's scoring charts.

Luka Jovic, who replaced the injured Benzema, enjoyed his best game as a Real Madrid player, assisting Vinicius for the first goal and scoring the second with a diving header.

Napoli surrendered the lead to lose 3-2 at home to Atalanta on Saturday, dropping from first to third as the gap between the top four sides in Serie A was squeezed to four points.

Luciano Spalletti's hosts recovered from a goal down and went in front early in the second half, only for the visiting Bergamo club to mount a comeback of their own and inflict a second league defeat of the season on the hosts.

The result saw Napoli, who had led the title race since week four, remain on 36 points, two behind new leaders AC Milan, one behind Inter Milan and two ahead of fourth-placed Atalanta.

(With input from agencies)