Everton won in Sam Allardyce's first match in charge, beating Huddersfield 2-0 thanks to Gylfi Sigurdsson and Dominic Calvert-Lewin goals.
The former England manager replaced caretaker boss David Unsworth this week after signing an 18-month contract. The Toffees, having been in the relegation zone last weekend, are now in the top half after two wins in a row.
Manchester United beat Arsenal 3-1 in one of the most entertaining games of the season. Jesse Lingard scored twice, with Paul Pogba being sent off - ruling him out of the Manchester derby.
Roberto Firmino scored twice as Liverpool beat Brighton 5-1 to climb to fourth in the table.
Tottenham had defender Davinson Sanchez sent off as they were held to a 1-1 draw by Watford.
- Report: Arsenal 1-3 Manchester United
- Report: Brighton 1-5 Liverpool
- Report: Everton 2-0 Huddersfield
- Report: Watford 1-1 Tottenham Hotspur
West Brom drew 0-0 with Crystal Palace in Alan Pardew's first game as Baggies manager.
Eden Hazard scored twice in an impressive performance as Chelsea came from behind to beat Newcastle 3-1.
Swansea dropped to the bottom of the Premier League table after losing 2-1 to fellow strugglers Stoke. Leicester beat in-form Burnley 1-0, thanks to Demarai Gray's early goal.
- Report: Chelsea 3-1 Newcastle
- Report: Leicester 1-0 Burnley
- Report: Stoke 2-1 Swansea
- Report: West Brom 0-0 Crystal Palace
In the FA Cup, non-league side Hereford are in the hat for the FA Cup third round, after drawing 1-1 at Fleetwood.
Scottish Premiership champions Celtic extended their domestic unbeaten run to 67 games thanks to a 5-1 win over Motherwell, with Odsonne Edouard scoring a hat-trick.
Kick-off in Hearts' game against Hamilton was delayed by 15 minutes after Tynecastle had to be evacuated at 14:00 GMT because of a faulty fire alarm being set off.
Sunderland's woes continued as they lost 3-1 to Reading in Chris Coleman's first home game in charge. The Black Cats have not won a home game in 2017 - a run of 21 games. To make matters worse, Callum McManaman was shown a second yellow card for handling the ball into the net.
Elsewhere in the Championship, Ipswich beat Nottingham Forest 4-2,Sheffield United lost 3-1 at Millwall and Michael Dawson scored an injury-time equaliser as Hull battled back to draw 2-2 with Sheffield Wednesday.
In Northern Ireland's Premiership, second-placed Crusaders beat Glentoran 1-0. Watch the day's goals here.
Barcelona remain unbeaten at the top of La Liga after being held to an entertaining 2-2 draw by Celta Vigo.
Bayern Munich are six points clear at the top in Germany after beating Hannover 3-1, with second-placed RB Leipzig being thrashed 4-0 at Hoffenheim.
Paris St-Germain lost for the first time in France's Ligue 1 this season, with former St Mirren loanee Stephane Bahoken scoring Strasbourg's winner in the 2-1 victory,
And the biggest scoring game of the day was in Scotland's Highland League, where Brora Rangers beat Fort William 16-0. Steven Mackay scored five of the goals.
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