Brighton continued their red-hot form by smashing rivals Crystal Palace 5-0, while Manchester City maintained their perfect record by beating Ipswich 3-2.
Arsenal edged Nottingham Forest 1-0 away from home, while Liverpool, Chelsea, Aston Villa and Tottenham also picked up hard-fought wins.
Here, Flashscore selects its Premier League Team of the Week – based solely on our player ratings system.
Goalkeeper
Emiliano Martinez (Chelsea) - 7.8
Martinez made four saves to contribute to Chelsea's 2-0 win and clean sheet at Everton, with his best denying Thierno Barry from close range.
He bravely attacked an aerial duel with James Tarkowski in the second half and had to be stretchered off and replaced by Mike Penders after 75 minutes.
Defenders
James Hill (Bournemouth) - 8.8
Hill was defensively resolute for Bournemouth in their straightforward 2-0 win over 10-man Sunderland.
The 24-year-old won nine of 10 duels contested and made seven clearances, while he was also strong on the ball.
No player had more touches (96), accurate passes into the final third (13) or progressive carries (8) than him.
Jan Paul van Hecke (Tottenham) - 8.2
Van Hecke provided Spurs a bit of quality in possession as they beat Coventry 3-1 to chalk up their first win of the campaign.
The Dutchman had 115 touches, 34 progressive carries and 10 progressive passes, while he also won 10 duels in the victory.
Olivier Boscagli (Brighton) - 8.9
Boscagli has become a dependable option for in-form Brighton and he kept that up in the dismantling of Palace.
The Frenchman made 13 passes into the final third and 12 progressive passes, while it was his ball that found Diego Gomez for his wonder strike from the halfway line.
Midfielders
Pedro Neto (Chelsea) - 9.2
Neto clinically netted both of Chelsea's goals at Everton towards the start and end of the second half.
No player in the match had more key passes (5) or touches in the opposition box (5) than the Portuguese.
Mateo Kovacic (Manchester City) - 8.4
Kovacic's hard work earned him an assist for Erling Haaland's first goal as City fended off a spirited Ipswich display.
The Croatian had three key passes and three successful dribbles for City, who remain top of the table.
Declan Rice (Arsenal) - 8.5
Rice grabbed the assist for Noni Madueke's winning goal for Arsenal in their gritty 1-0 win at Nottingham Forest.
England star Rice was keen to get busy at the City Ground, making three key passes, completing 93 of 99 passes and carrying the ball 18 times.
Alex Iwobi (Fulham) - 9.1
Fulham's 1-0 victory over Hull was powered by an industrious showing by Iwobi, who whipped in the game-winner.
Iwobi took four shots inside the box, created two big chances and made 15 progressive passes.
Forwards
Charalampos Kostoulas (Brighton) - 8.4
Kostoulas was all over it for Brighton with a goal and an assist to his name in a strong attacking performance.
The Greek striker took four shots in total and also completed three dribbles.
Erling Haaland (Manchester City) - 9.3
Two goals for Haaland against Ipswich took the Norwegian's tally up to eight in the first seven league games.
After a tame start, Haaland took five shots and created two big chances from three key passes in another strong attacking performance.
Evanilson (Bournemouth) - 9.4
Evanilson played a big role in Bournemouth's win, including drawing the foul that saw Sunderland reduced to 10 men.
The Brazilian rounded the goalkeeper brilliantly to double the Cherries' lead after unselfishly assisting James Tavernier's opener.
Evanilson ended the game with 11 touches in the Sunderland box, one big chance created and nine duels won.
