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Arsenal eased fears of being dragged into a relegation battle with a stunning 3-1 win over Chelsea on Saturday, as Manchester United's Premier League title challenge stumbled after they conceded a late equaliser to draw at Leicester.
Everton moved into second place, two points behind leaders Liverpool with a 1-0 win at Sheffield United, while Manchester City climbed to fifth place after beating Newcastle 2-0.
Liverpool will go five points clear of Everton if they beat struggling West Brom on Sunday.
Mikel Arteta led Arsenal to win the FA Cup the last time they faced Chelsea in August, but less than five months on the Spaniard was under intense pressure after a run of one win in 10 league games.
Arteta had bemoaned his side's fortune in recent weeks, but the Gunners' luck turned on a night when he gave youngsters Gabriel Martinelli and Emile Smith Rowe the chance to shine in the absence of more experienced figures such as David Luiz, Willian and Pierre-Emerick Aubameyang.
"It's a really big win for us," said Arteta. "Hopefully it is going to be a turning point and elevate the level of confidence in the team."
Kieran Tierney won a soft penalty for a push by Reece James and Alexandre Lacazette slotted home the spot-kick to open the scoring on 34 minutes.
Granit Xhaka then answered his critics after being stupidly sent off in a 1-0 defeat by Burnley earlier this month with a brilliant free-kick to double Arsenal's lead just before half-time.
A third consecutive away loss for Chelsea further damages their chances of competing for the title and there was no way back for Frank Lampard's men once Bukayo Saka chipped in off the inside of the post 11 minutes after the break.
"It's not good enough," said Lampard. "The players have got to take responsibility."
Tammy Abraham did pull a goal back five minutes from time and Chelsea could have set up a grandstand finish in stoppage time, but Jorginho's penalty was saved by Bernd Leno.
Victory lifts Arsenal up to 14th, six points clear of the relegation zone, while Chelsea drop down to sixth on goal difference.
- Man Utd miss out -
Manchester United missed out on equalling a Premier League record of 11 straight away wins as for once this season they paid for not finishing strongly in a dramatic 2-2 draw.
Ole Gunnar Solskjaer's men had come from behind in each of their previous away league games this season, but twice went in front at the King Power Stadium through Marcus Rashford midway through the first half and Bruno Fernandes 11 minutes from time.
"One point is not the worst result but we are disappointed we didn't get away with three," said Solskjaer.
Harvey Barnes' blistering strike levelled for Leicester before half-time and United were undone by Jamie Vardy's movement in the box as the veteran striker latched onto Ayoze Perez's cross and saw his shot deflect in off the unfortunate Axel Tuanzebe.
At Bramall Lane, Gylfi Sigurdsson killed off the bottom of the table Blades on 80 minutes with a clinical finish.
That sealed Everton's fourth successive league win and set up a significant clash with Manchester City on Monday.
"This team has a lot of spirit. I'm really pleased to manage these players," Everton boss Carlo Ancelotti said.
City extended their unbeaten league run to six matches with a comfortable success at the Etihad Stadium.
Ilkay Gundogan put Pep Guardiola's side ahead in the 14th minute with a close-range finish from Raheem Sterling's pass.
City doubled their lead in the 55th minute after Newcastle's Miguel Almiron gave the ball away just outside his own area.
Despite a desperate attempt to clear by Federico Fernandez, the ball rolled straight to Ferran Torres and the Spanish winger fired home.
"That is the tempo we need to play," Guardiola said. "There are weird results for everyone this season. You have to be calm in the good and the bad moments."
Aston Villa are another unlikely challenger for the top four as they eased past Crystal Palace 3-0 despite playing the full second half a man down after Tyrone Mings' red card.
Bertrand Traore gave Villa the perfect start but Mings made his teammates work hard for the win when he was sent off for two clashes with Wilfried Zaha.
Ignoring that setback, Kortney Hause and Anwar El Ghazi wrapped up the points for Villa.
Fulham edged to within a point of safety with a 0-0 draw at home with Southampton.