Striker Glenn Murray scored a brace and Jose Izquierdo curled in a shot from outside the box to lift promoted Brighton to 10th in the standings, leaving West Ham in 17th just above the relegation zone.
Goals from Curtis Davies and Robert Koren earned HullCity a place in the FA Cup quarter-finals with a 2-1 replay win at home to Brighton and Hove Albion on Monday.
A howler by Manchester United goalkeeper David De Gea gifted West Ham United three vital points in their battle against relegation as the hosts secured a 1-0 Premier League win.
Harry Kane became Tottenham's joint fifth highest scorer as he helped his side earn a 2-1 Premier League victory over Brighton & Hove Albion on Saturday.
Southampton clinched a thrilling comeback draw against Tottenham Hotspurs in their Premier League encounter on Saturday.
IMAGES from the English Premier League matches played on Saturday
IMAGES from the English Premier League matches played on Saturday
Three months after the last ball was kicked, the Premier League emerges from the shadow of the COVID-19 pandemic this week for what will be a 92-match slog to the finish.
Chelsea paid a heavy price for a 3-2 defeat at West Ham United as first Liverpool, then Manchester City, leapfrogged them in the English Premier League title race on Saturday, with City ending the day on top for the first time this season.
James Rodriguez netted twice and Dominic Calvert-Lewin became the first Everton player to score in the opening four matches of a Premier League season as they beat Brighton & Hove Albion 4-2 on Saturday to stay top of the table with a maximum 12 points.
Bukayo Saka scored either side of halftime as Arsenal crushed second-bottom Burnley 5-0.
Holders Manchester City were eliminated from the League Cup by West Ham United after a penalty shootout at London Stadium on Wednesday, ending Pep Guardiola's team's four-year domination of the competition.
Images from Saturday's action in the Premier League.
Liverpool a dramatic 2-1 victory over Leicester City at Anfield, thus maintaining the league leaders' 100 per cent start
Romelu Lukaku scored for Chelsea in a 5-1 FA Cup third-round victory
Images from the English Premier League matches played on Sunday.
A summary of the UEFA Champions League Group Stage action, on Wednesday.
With United unable to sign a replacement, the pressure will be on 21-year-old England forward Marcus Rashford to deliver the goals in a more central role than he has previously operated in.
Leicester City's traumatic week ended with a 1-0 win at Cardiff City although the result was never the chief concern on a day when the tributes flowed for the Midlands club's late owner Vichai Srivaddhanaprabha who died in a helicopter crash.
Timo Werner scored his first goal of the season as a much-changed Chelsea side crept into the fourth round of the League Cup by beating Aston Villa 4-3 on penalties after the Stamford Bridge clash ended 1-1 on Wednesday.
Saturday's clash between Manchester United and Tottenham Hotspur at Old Trafford is already shaping up as an early-season eliminator to challenge runaway leaders Manchester City for the Premier League title.
Defeats at Manchester City and Brighton & Hove Albion had left Arsenal down in 11th place but their victory on the south coast lifted them to ninth with 43 points from 31 games -- eight behind fourth-placed Chelsea who were playing City later.
Manchester United's current malaise was laid bare as they struggled past third-tier Rochdale 5-3 on penalties after a 1-1 draw in the League Cup third round.
IMAGES from the English Premier League matches played on Saturday.
The 13-year-old Burnley fan who made a racial slur against Spurs' Son Heung-Min will be made to work in conjunction with Kick It Out and Burnley FC in the Community programs.
Images from the English Premier League matches played on Sunday night
Cristiano Ronaldo scored twice as Juventus strolled to a 3-0 home win over bottom side Crotone in the Italian Serie A on Monday, with the victory taking the champions up to third in the standings.
Last week clubs were told any return to complete the season would have to be with games played behind closed doors and at neutral venues - to limit the risk of supporters turning up outside grounds. But that idea had been rejected by some of the clubs facing the threat of relegation.
Zidane plays down Ronaldo injury; Liverpool's Gomez sidelined after surgey
Roberto Firmino's 90th-minute header sent Liverpool back to the top of the Premier League with a 2-1 victory over Tottenham Hotspur, whose 11-match unbeaten run came to an end on Wednesday.
Headers by Romelu Lukaku and Nemanja Matic earned Manchester United an unconvincing 2-0 victory over Brighton and Hove Albion in a low-key FA Cup quarter-final played in freezing conditions on Saturday.
Hazard's dribbling and movement, on and off the ball, constantly posed questions for the Liverpool defence and the winger, who was so central to Chelsea's title triumph last year, certainly looks back up to full speed.
Although Spurs always looked more comfortable on the ball it was Sean Dyche's side, who have just a point from their opening five games, who had come the closest.
A round-up of Saturday's action in the Premier League.
Manchester United remain winless at home in the league this season after Arsenal enjoyed their first win at Old Trafford
The price eclipsed the A$425,000 achieved by the late Don Bradman's baggy green when it was sold in 2003.
Images from Saturday's action in the English Premier League.
Liam Delap, the son of former Stoke City defender Rory, scored the opener for Pep Guardiola's side in the 2-1 win at the Etihad Stadium
Here are five talking points from the weekend's action:
News of all that's transpired on and off the football field
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