LONDON -- Liverpool piled on the misery for Manchester City as the Premier League leaders beat the troubled champions 2-0 at Anfield, while Manchester United boss Ruben Amorim earned his first league win with a 4-0 rout of Everton on Sunday.

Arne Slot's side moved nine points clear of second-placed Arsenal after Cody Gakpo's first-half opener and Mohamed Salah's late penalty dealt another blow to reeling City, who are languishing 11 points behind Liverpool in fifth place.

City have lost four successive top-flight games for the first time since 2008, making them the first Premier League champions to endure such a dismal run the season after claiming the title.

City have clawed back significant deficits to win the Premier League in the Guardiola era, but they have never managed to lift the title after being behind by more than 10 points.

City's seven-game winless run ranks as boss Pep Guardiola's longest barren streak in his glittering managerial career.

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Just weeks after he signed a new two-year contract, Liverpool fans taunted Guardiola with chants of "you're getting sacked in the morning", prompting a defiant response from the Spaniard, who held up six fingers to illustrate the number of titles he has won with City.

"The first 20 minutes Liverpool were unstoppable. We tried to play with a lot of control and passes, but it was difficult to take it," Guardiola said.

"We'll reset and start from zero. It is difficult to believe it. I rely a lot on these players. We'll see what happens by the end of the season."

Liverpool have won 18 of their 20 games in all competitions since Slot replaced Jurgen Klopp in the close-season.

With 11 victories from their 13 Premier League matches, Liverpool are firm favorites to win the title for the first time since 2020.

"We came close to perfection. That's the only way to beat a quality team like City," Slot said.

"We have to stay sharp. I don't think anyone, including me, would have predicted this -- to win so much with all the difficult teams we have played already."

City's defense was in disarray right from the start and when Salah curled a 12th minute shot towards the far post, Gakpo pounced to poke home from virtually on the line.

Salah's 78th-minute penalty, awarded for keeper Stefan Ortega's foul on Luis Diaz, was a dagger in the heart of City's title hopes.

Amorim stole the spotlight in Sunday's early games by extending his unbeaten start with United to three matches.

United were held to a 1-1 draw at Ipswich in his first Premier League game last Sunday, before the Portuguese boss earned his maiden win with United in a 3-2 success against Bodo/Glimt in the Europa League on Thursday.

- Man Utd power surge -

The 39-year-old, who arrived from Sporting Lisbon to replace the sacked Erik ten Hag in November, has warned United would "suffer for a long period" before they can expect to challenge for the title.

This was the most encouraging result of Amorim's brief time at ninth-placed United.

Marcus Rashford's 34th-minute drive from the edge of the area took a deflection off Jarrad Branthwaite before flashing into the net.

United struck again seven minutes later as Branthwaite lost possession to Amad Diallo and Bruno Fernandes teed up Joshua Zirkzee to convert with ease.

Rashford underlined United's superiority just 20 seconds after the interval as he applied a cool finish to Diallo's incisive pass, before Zirkee struck again in the 64th minute with a composed strike.

"The result was good but we were pragmatic. It was not pretty," Amorim said. "It is a rollercoaster. We have some moments when we are good but then we have moments when we have to suffer."

At Stamford Bridge, Chelsea extended their unbeaten run in all competitions to six games with a 3-0 win against Aston Villa, whose dismal winless streak reached eight matches.

Enzo Maresca's men look capable of securing Champions League qualification after a third successive win in the space of eight days moved them level on points with second-placed Arsenal.

Nicolas Jackson and Enzo Fernandez scored in the first half before Cole Palmer struck in the closing stages.

Seventh-placed Tottenham's top-four hopes were dented by a 1-1 draw against 10-man Fulham.

Brennan Johnson slotted Tottenham into the lead from Timo Werner's 54th-minute pass, but Tom Cairney curled Fulham's equalizer into the far corner after 67 minutes.

Cairney was sent off with seven minutes left after his foul on Dejan Kulusevski was upgraded from referee Darren Bond's initial yellow card to a red after VAR intervened.

© Agence France-Presse