Opening the season, the champions Arsenal kicked off the defence of their title with a comfortable 3-0 win over newly-promoted Coventry.
But fellow newcomers Hull made a winning start by beating Manchester United 2-0, while Ipswich recorded a late 2-1 victory over Sunderland.
Elsewhere, Chelsea entertained in a 3-2 win against London rivals Fulham, as did Brentford as they hammered Tottenham 3-0.
Based on Flashscore's player ratings system, it's time to select the first Premier League Team of the Week of the season.
Goalkeeper
Konstantinos Tzolakis (Hull) - 8.2
New goalkeeper signing Tzolakis made an immediate impact as Hull stunned United on their Premier League return.
Keeping a clean sheet, the Greek stopper made five saves and four high claims in a calm outing.
Defenders
White was a threat with his overlapping runs down Arsenal's right flank against newcomers Coventry.
He saw plenty of the ball with 94 touches and assisted Martin Odegaard's goal with a cutback.
Maxence Lacroix (Chelsea) - 8.6
Summer acquisition Lacroix looked assured in a back three for Chelsea against Fulham and was handy at both ends of the pitch.
Lacroix won eight duels and made two last-man tackles, but looked silky when he took on his man and cut the ball back for Morgan Rogers' strike.
Olivier Boscagli (Brighton) - 8.7
Boscagli had an almost faultless display in the Brighton defence as they hammered Aston Villa 4-0 after a devastating first half.
The Frenchman completed all but one of his 65 passes during the contest and made a game-high eight progressive passes.
Midfielders
Bukayo Saka (Arsenal) - 8.3
Appearing free of injury, Saka looked like his old self with a sharp performance for the champions.
Saka doubled Arsenal's lead by staying alert to tuck away the rebound following a parry from Carl Rushworth.
Cole Palmer (Chelsea) - 9.2
Ice-cold Palmer took full control for Chelsea with a really silky performance that only a few can replicate.
Completing a game-high five dribbles, Palmer ran the show as he came away from Craven Cottage with a goal and an assist.
Marc Guehi (Manchester City) - 8.5
Guehi was deployed in an unconventional midfield role for City as Enzo Maresca still tinkers to find his best set-up.
He won eight duels, created one big chance and headed in City's equaliser to get them back in the game late on.
Jack Hinshelwood (Brighton) - 9.0
Hinshelwood popped up in all the right places for Brighton in their emphatic dismantling of Villa.
The 21-year-old's first saw him head in unmarked before picking up a loose ball and notching his second just 79 seconds later.
Morgan Rogers (Chelsea) - 8.9
Debutant Rogers showed glimpses of why Chelsea shelled out £117 million this summer to bring him in.
The England star slotted in a debut goal thanks to Lacroix's excellent work, while winning eight duels and completing three dribbles.
Forwards
Joao Pedro (Chelsea) - 8.7
Just 31 seconds was all it took for Joao Pedro to open his Chelsea account for the season.
A menacing attacking performance saw him also notch an assist for Palmer's effort early in the second half.
Emersonn hit the ground running for Ipswich by scoring on his debut and helping them make a winning start back in the top flight.
He bundled in their opener and won seven duels as he made himself a nuisance throughout.
English Premier League
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