Relegation-threatened Southampton remain in the bottom three despite drawing 1-1 with Tottenham at St Mary’s.
Sergio Aguero scored a hat-trick as Manchester City beat Newcastle 3-1 in Saturday's late game in the Premier League.
Javier Hernandez rescued a point for West Ham after cancelling out Ryan Fraser's opener to secure a 1-1 draw against Bournemouth.
Paul Lambert kicked off his Stoke City reign with a comfortable win over struggling Huddersfield at the Bet365 Stadium.
Oumar Niasse cancelled out Jay Rodriguez's opener as Everton were held to a 1-1 by West Brom at Goodison Park.
Goals from Jamie Vardy and Riyad Mahrez helped Leicester secure a routine 2-0 victory over Watford at the King Power on Saturday.
Anthony Martial rifled in the only goal of the game as Manchester United edged to a 1-0 victory over Burnley at Turf Moor.
Arsenal scored four times in the opening 22 minutes as they swept aside Crystal Palace 4-1 at the Emirates Stadium.
Belgian international Eden Hazard scored a brace as Chelsea beat Brighton 4-0 at the Amex Stadium.
New Stoke City boss Paul Lambert watched on as his struggling side were well beaten 3-0 at Manchester United on Monday night.
Leaders Manchester City slipped to their first Premier League defeat of the season as a rampant Liverpool edged them out 4-3 at Anfield.
How did the players compare
Manchester City suffered their first Premier League defeat of the season as they lost out 4-3 to Liverpool in an Anfield thriller.
Bournemouth eased their relegation concerns as they came from behind to defeat top-four chasing Arsenal 2-1 at the Vitality Stadium.
England striker Harry Kane scored a brace as Tottenham beat Everton 4-0 at Wembley on Saturday evening.
Newcastle were left to rue a failure to make early dominance count as they came from behind to draw with Swansea at St James' Park.
Jonny Evans and Craig Dawson got the goals as West Brom beat Brighton 2-0 to secure Alan Pardew his first league win as Baggies boss.
Marko Arnautovic was outstanding as West Ham continued their push up the Premier League with a 4-1 win at Huddersfield.
Abdoulaye Doucoure scored controversially in injury time as Watford fought back from two goals down to earn a point against Southampto.
Bakary Sako scored the crucial goal as Crystal Palace moved five points clear of the relegation zone by beating Burnley 1-0.
Ryan Harley netted the winner as Exeter moved above Coventry in Sky Bet League Two with a narrow 1-0 victory at St James Park.