Tottenham were held at home by Sheffield United while Everton piled more pressure on Southampton boss Ralph Hasenhuttl.
Premier League results
- Chelsea 2-0 Crystal Palace - Report & highlights
- Burnley 3-0 West Ham United
- Newcastle United 2-1 Bournemouth
- Southampton 1-2 Everton
- Tottenham Hotspur 1-1 Sheffield United
- Leicester City 2-0 Arsenal
Red-hot Jame Vardy piled the pressure on Arsenal boss Unai Emery as the Leicester striker continued to haunt the Gunners.
The forward scored his ninth goal in nine games against the Gunners to inspire the Foxes to a 2-0 win and into second in the Premier League.
Vardy, the top flight's 11-goal leading scorer, also set up James Maddison's clincher as Emery's side slumped to a limp defeat at the King Power Stadium.
Alexandre Lacazette wasted Arsenal's best chance and Pierre-Emerick Aubameyang had a goal disallowed but the visitors were poor.
The Gunners, winless in the Premier League for over a month, slipped eight points behind the top four with Emery's position under increasing scrutiny.
Leicester now sit five points behind leaders Liverpool - who host Manchester City on Sunday - after a deserved fifth straight win.
It's a worst Premier League start in 11 years for Tottenham who could arguably have lost at home against a fine Sheffield United side, who had a goal ruled out by the narrowest of margins on a three-minute VAR review.
Chris Wilder's Blades matched Spurs all the way, even when Son Heung-min put the hosts ahead just before the hour mark they responded in a couple of minutes with a goal from David McGoldrick. That strike, however, was ruled out by VAR after a lengthy review.
George Baldock did put the visitors level 12 minutes from the end, although even that goal survived another lengthy check by the video replay, but it stood to secure a deserved point for United.
The Blades remain unbeaten on the road in the Premier League this season, and Mauricio Pochettino remains in some trouble with his side unable to find a consistent level of performance in the league.
Chelsea made it six straight league victories for the first time in three years with a comfortable 2-0 win over Crystal Palace at Stamford Bridge.
England striker Tammy Abraham broke the deadlock seven minutes into the second half with his 11th goal of the season, with Christian Pulisic wrapping up the points 11 minutes from time with his fifth goal in his last five appearances.
The two favourites to be sacked clashed at St Mary's and it is Southampton boss Ralph Hasenhuttl who will be feeling the pressure after Marco Silva's Everton came away with a crucial three points at their fellow strugglers.
Tom Davies gave the Toffees the perfect start with an early goal in a first half they dominated, but Danny Ings levelled as Saints produced a much improved display in the second 45 minutes.
It was end-to-end stuff but Richarlison bagged the winner for the visitors, who go flying up into 13th in the table above Manchester United and level on points with Tottenham, while Saints and Hasenhuttl remain deep in trouble.
More misery for Manuel Pellegrini as well as his West Ham side continued their alarming slide with a fourth defeat in their six-game winless run in the Premier League after another tepid performance.
Ashley Barnes and Chris Wood scored in the first half, with Wood also having a goal ruled out by VAR, before goalkeeper Roberto Jimenez punched the ball into his own net to cap off a shocker for him.
It was a welcome win for Sean Dyche's side after three straight defeats, but it slipped the Hammers nearer to the relegation zone as the pressure mounts on West Ham boss Pellegrini.
Harry Wilson gave Bournemouth a fast start up at St James' park when he opened the scoring just inside the 15-minute mark, but DeAndre Yedlin's strike just before half time ensured the hosts went in level at the break.
Ciaran Clark put Newcastle ahead seven minutes into the second half, and they held on for the three points despite chances coming thick and fast at both ends.
The Cherries dominated possession but got just three shots on target from their 67 percent of the ball, while Steve Bruce's side managed a whopping nine efforts on target from half as much of the ball.
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