Real Madrid piled renewed pressure on Barcelona coach Ronald Koeman as David Alaba scored a scintillating goal to help seal a 2-1 victory in the Clasico on Sunday.

But Real Sociedad regained their place at the top of La Liga after holding off Atletico Madrid's late comeback to draw 2-2 in a thrilling game at the Wanda Metropolitano.

Luis Suarez scored twice in the second half, including a penalty, to salvage a point for Atleti, who edge up to fourth. That match had more bearing at the top of the table, a sign of the times perhaps for La Liga, which could prove more open to challengers this season than for a long time.

Alaba's bending shot had Real Madrid in front for the majority of an end-to-end contest a Camp Nou, with Lucas Vazquez making it two in injury-time before Sergio Aguero tapped in his first goal for Barcelona with seconds left.

Barca have now lost a fourth consecutive El Clasico for the first time since 1965 and dropped to ninth in La Liga, five points behind Madrid, who trail Real Sociedad by one. 

"These games are always close," said Koeman. "They have their game, we have ours and the details decide the result. It's a shame because we had the opportunities to score."

Madrid coach Carlo Ancelotti said: "We played against a great team, we have suffered, but we were able to cope."

In England, Ole Gunnar Solskjaer rued his "darkest day" as Manchester United manager after Mohamed Salah's hat-trick swept Liverpool to a stunning 5-0 win over their arch rivals at Old Trafford.

Ten years after Manchester City's infamous 6-1 victory at Old Trafford, Liverpool inflicted one of the most embarrassing losses United have ever suffered. Mohamed Salah scored a hat-trick, while Naby Keita and Diogo Jota also netted for the rampant visitors.

It was Liverpool's biggest win against United since 1925 and moved them seven points clear of Solskjaer's side in the Premier League table.

Second-placed Liverpool are just one point behind leaders Chelsea as they chase the title – an ambition which looks completely beyond hapless United after this wretched afternoon.

"It is not easy to say something apart from it is the darkest day I have had leading these players," Solskjaer said. "You can look at last season when we lost to Spurs 6-1, but this is miles worse for me as a Manchester lad."

United are languishing in seventh place after a fourth successive league game without a win, a dismal streak that includes three defeats.

In Italy, Napoli's 100 percent start to the Serie A season came to an end on Sunday with a goalless draw at Roma which halted their winning run at eight matches.

Napoli retake top spot in the Italian top flight but are level on 25 points with AC Milan following their hard-fought win at Bologna on Saturday.

The draw means Roma keep the record for the most wins from the start of a Serie A season, with 10 consecutive victories in 2013/14.

Both sides will be ruing missed chances which could have decided a tight, at times poorly tempered, match between two rivals which saw both coaches sent off.

Roma boss Jose Mourinho was sent to the stands for dissent with nine minutes left while an incredulous Luciano Spalletti was shown a red card for what referee Davide Massa thought was sarcastic applause.

Paulo Dybala saved Juventus on Sunday with a controversial late penalty which earned his team a 1-1 draw at Inter Milan. 

Inter thought they had won the match thanks to a goal from Edin Dzeko, but Dybala slotted home his spot-kick with a minute left. His leveler came in his first appearance after a month out with a thigh injury, the 27-year-old coming on as a substitute in the 63rd minute. 

Juve are up to sixth on 15 points, level with Atalanta and Fiorentina, while champions Inter are seven points behind Napoli and city rivals AC Milan in third place.

In France, Lionel Messi was kept quiet as 10-man Paris Saint-Germain settled for a 0-0 draw with bitter rivals Marseille in a heated atmosphere in Ligue 1.

The meeting of French football's biggest rivals was briefly held up on more than one occasion as objects were thrown from the stands when PSG players went to take corner kicks.

There was another interruption in the second half when one young man invaded the pitch and approached Messi before being escorted off by a legion of security staff.

It was that sort of night for PSG, who could not get into their stride and were reduced to 10 men when Achraf Hakimi was sent off in the second half following a VAR review for a last-man challenge on Cengiz Under just outside the box.

The game was also marked by two goals that were disallowed in the first half for tight VAR offside decisions, one an own-goal by Marseille defender Luan Peres and another at the opposite end from Arkadiusz Milik.

It is a perfectly acceptable result for Mauricio Pochettino's side, who have lost just one of their opening 11 matches in Ligue 1 and are seven points clear at the top from Lens in second.