Manchester United battled back from two goals down to beat Newcastle United 3-2 at Old Trafford on Saturday as a 90th-minute winner from Alexis Sanchez completed a spirited comeback to ease the pressure on manager Jose Mourinho.
Chelsea goalkeeper Kepa Arrizabalaga remains the club's first choice but manager Maurizio Sarri is still uncertain if the Spaniard will be recalled to the starting team for Sunday's Premier League trip to Fulham.
Images from the English Premier League matches played on Tuesday
Tottenham Hotspur claimed a first victory at Chelsea for 28 years with Dele Alli scoring twice in the second half as they came back to win 3-1 and cement fourth place in the Premier League on Sunday.
Liverpool manager Juergen Klopp acknowledged that they would have to defend better in the visit to Stamford Bridge to stop Eden Hazard reprising the sort of solo brilliance that propelled Chelsea to victory at Anfield on Wednesday.
Liverpool took over at the top of the Premier League table despite being held to a 0-0 draw against Manchester United in a scrappy match on Sunday.
Romelu Lukaku's 50th league goal for Everton put them on the way to a deserved 2-0 victory over West Ham United on Sunday, ending a run of four league games without a win. It kept the Merseysiders sixth in the Premier League and West Ham in the bottom five.
Chelsea lost their 100 per cent Premier League record when London rivals West Ham United held them to a 0-0 draw on Sunday.
Images from the English Premier League matches played on Saturday
The centre-back has not played since Sarri took over from Antonio Conte at the start of the season, and says he could call time on his career at Stamford Bridge when the transfer window reopens if his situation does not improve.
Another Liverpool great, Graeme Souness, said Klopp had produced a "fabulous" side.
Leicester City manager Claudio Ranieri has asked for a change in mentality to revive the club's Premier League campaign which is in stark contrast to their impressive Champions League form.
Liverpool continued their perfect start to the season to stay top of the Premier League after a goal in each half gave them a 2-1 victory over Tottenham Hotspur at Wembley on Saturday.
Tottenham went ahead through Sanchez who scored his first goal for the London club by meeting Eriksen's whipped cross with a diving header in the 33rd minute, although Leicester's players complained he was in an offside position.
IMAGES from the English Premier League matches played on Saturday
Chelsea ended their slump with a win over Arsenal while seemingly invincible Manchester City lost their 100 per cent record to West Ham United on a day of contrasting fortunes for the Premier League title favourites on Saturday.
'Did the Moneyball philosophy get redefined in the domain of the cash-rich IPL, which has become an integral part of the cricketing ecosystem?' asks Atanu Biswas.
Romelu Lukaku struck twice as Manchester United returned to winning ways after two successive Premier League losses with a 2-0 victory over Burnley at Turf Moor on Sunday.
The north London outfit were brushed aside by a dominant City side in last Sunday's League Cup final with Pep Guardiola's team converting all three of their shots on target to win 3-0 while Arsenal failed to convert either of their chances.
Champions Manchester City will expect to get back to winning ways at home to Newcastle United in a match which pits Pep Guardiola against his fellow Spaniard Rafa Benitez.
I don't think we can do a Leicester. I am realistic, says Everton manager
Chelsea kept up their 100 percent start to the English Premier League season by snatching a 2-1 win at a stubborn Newcastle United on Sunday, grabbing victory thanks to a late own goal by DeAndre Yedlin.
Sergio Aguero and Kevin De Bruyne put on an attacking masterclass to help City rout Leicester City 5-1.
Daryl Janmaat, Gerard Deulofeu and Roberto Pereyra all scored late on in response to Eden Hazard dragging Chelsea back into the game with a curler in the 82nd minute after Tiemoue Bakayoko was sent off for a second booking on the half-hour.
Chelsea have completed the signing of Basel's Egyptian winger Mohamed Salah, the Premier League club said on their website on Sunday.
Manchester United will be without world record signing Paul Pogba for their Premier League opener against Bournemouth on Sunday due to a suspension, the Football Association said on Friday.
Southampton were left in the Premier League's bottom three after losing an early lead to draw 1-1 at home to fifth-placed Tottenham Hotspur on Sunday.
Chelsea kept up their pursuit of the Premier League's top three clubs with a 1-0 win away to London rivals Crystal Palace on Sunday, thanks to a strike by N'Golo Kante early in the second half.
Tottenham Hotspur routed Bournemouth 5-0 as they leapfrogged City into second place in the league, six points behind leaders Liverpool who thrashed Newcastle United 4-0.
Manchester City suffered their first home Premier League loss in eight months as a shock 3-2 defeat by Crystal Palace on Saturday left Pep Guardiola's champions trailing leaders Liverpool by four points.
A rampant Harry Kane netted four goals and livewire Son Heung-Min scored twice as Tottenham Hotspur thrashed Leicester City 6-1 in an action-packed Premier League clash on Thursday.
Departing captain John Terry led his Chelsea champions to a rip-roaring 4-3 victory over Watford on Monday, scoring the first goal on an evening of celebration, fireworks and streamers rather than vintage football at Stamford Bridge.
The victory, Chelsea's 28th of the season, put the long-time league leaders 10 points clear of second-placed Tottenham Hotspur, who have only three games left to play.
Images from the English Premier League London derby played between Arsenal and Chelsea at the Emirates on Wednesday
Champions Manchester City have won their last 10 home league matches scoring a total of 36 goals.
City have 89 points, one more than rivals Liverpool, with both teams having three games to play -- and none of them against top six opponents.
Alexis Sanchez and Olivier Giroud were on target as Arsenal won 2-0 at Southampton on Wednesday to move up to fifth in the Premier League and fuel their hopes of a late push for the top four.