Liverpool reestablished their five-point lead at the top of the Premier League table as they beat Chelsea 2-1 on Sunday.
Manchester United lost 2-0 at West Ham United and Arsenal twice came from behind to beat Aston Villa 3-2 at the Emirates Stadium.
Wolverhampton Wanderers, meanwhile, remain without a win all season after they drew 1-1 at Crystal Palace.
Here is the table in full following the weekend's action:
Matchday 6 Results
Southampton 1-3 Bournemouth
Leicester City 2-1 Tottenham Hotspur
Burnley 2-0 Norwich City
Everton 0-2 Sheffield United
Manchester City 8-0 Watford
Newcastle United 0-0 Brighton and Hove Albion
Crystal Palace 1-1 Wolverhampton Wanderers
West Ham United 2-0 Manchester United
Arsenal 3-2 Aston Villa
Chelsea 1-2 Liverpool
Liverpool made the most of set-pieces to pick up another three points against Chelsea and maintain their perfect start to the new campaign.
A clever free-kick routine from the edge of Chelsea's box in the 14th minute saw Trent Alexander-Arnold whip home the opener after Mohamed Salah's lay-off.
And Roberto Firmino then rose highest to head home Andy Robertson's free-kick on the half-hour minutes after VAR ruled out a Cesar Azpilicueta goal due to a Mason Mount offside in the build-up.
After Liverpool's second, Chelsea were largely the better side and threatened to take a point in the dying stages after N'Golo Kante's brilliant finish from the edge of the box 20 minutes from time.
The Reds held on, though, and continue to set a furious pace in the title race:
United, meanwhile, remain wholly unconvincing.
They started the season well when they beat Chelsea 4-0, but ever since, Ole Gunnar Solskjaer's side have struggled.
And West Ham were deserving winners on Sunday at the London Stadium.
Andriy Yarmolenko opened the scoring on the stroke of half-time, finishing low past David De Gea in the United goal.
Aaron Cresswell then sealed the points for the Hammers six minutes from time when he placed a brilliant free kick into the top corner.
To make matters worse for United, they lost Marcus Rashford to injury just after the hour:
It was almost a torrid day for Arsenal at home, but Pierre-Emerick Aubameyang's stunning free-kick six minutes from time for the 10-man Gunners completed an impressive turnaround.
John McGinn opened the scoring for the visitors in the 20th minute and Ainsley Maitland-Niles was then shown a second yellow card just before the break:
Before the hour, Arsenal then equalised through Nicolas Pepe's penalty—his first goal for the club—only for Wesley to put Villa back in front barely a minute later.
Goals in the final 10 minutes from substitute Calum Chambers and then Aubameyang earned Arsenal all three points and moved them into fourth.
Wolves fell short again in their bid for a first win of the season, but it could have been worse.
Leander Dendoncker's own goal gave Palace the lead at Selhurst Park just after the break, and Romain Saiss was then sent off 17 minutes from time.
But Diogo Jota's close-range finish deep into stoppage time earned Wolves a point.