Both Manchester United and City enjoyed big wins against Ipswich and Crystal Palace, respectively, while Chelsea edged Brighton in a seven-goal thriller.
Elsewhere, Sunderland picked up their first win after beating Fulham, Hull maintained their winning start with a victory at Coventry and Newcastle sealed their first league triumph under Matthias Jaissle by beating Tottenham.
Here, Flashscore selects its Premier League Team of the Week - based on our player ratings system.
Goalkeeper
Konstantinos Tzolakis (Hull) - 8.1
For the second week in a row, Hull goalkeeper Tzolakis makes our side after yet another impressive performance.
The shot-stopper was on form for the Tigers' 1-0 victory away at Coventry, making three saves to ensure his team kept another clean sheet and made it two wins from two Premier League games.
Defenders
Ruben Dias (Manchester City) - 8.1
The first of two Manchester City defenders to make our side, Dias excelled in a 4-1 win away to Crystal Palace.
The Portuguese international won four duels, made one tackle, four clearances, six recoveries and one interception to secure an 8.1 Flashscore rating.
Marc Guehi (Manchester City) - 8.7
Dias' partner Guehi was equally effective during the win, contributing with four recoveries, three clearances and two interceptions - but his work on the ball particularly stood out.
Guehi led the match for accurate passes, passes into the final third, long balls and progressive passes, highlighting his importance to Enzo Maresca's new-look City side.
Lewis Hall (Newcastle) - 9.0
Newcastle enjoyed their first win under Jaissle on Saturday evening after defeating Spurs 2-0 at the Tottenham Hotspur Stadium.
Hall was the standout performer in London, providing excellent defensive cover while also influencing the match higher up the pitch.
The left-back won seven duels, made four blocks, six clearances and one interception; in attack, Hall provided three accurate crosses, eight progressive passes and one key pass.
Midifelders
Bruno Fernandes (Manchester United) - 10
Manchester United captain Fernandes excelled in their 5-2 thrashing of Ipswich, picking up Flashscore's first perfect 10 rating for the Premier League season.
Fernandes was on top form for the Red Devils and netted a hat-trick at Old Trafford before turning provider for Bryan Mbeumo's late goal.
The midfielder's perfect rating was the highest of any in the Premier League over the weekend - which makes Fernandes our Player of the Week.
Granit Xhaka (Sunderland) - 8.6
Sunderland got their first win of the season following a narrow 1-0 victory against Fulham on Saturday afternoon, with Xhaka instrumental to their success once again.
The Black Cats' captain put on a brilliant midfield showcase with four key passes, two big chances created and 10 progressive passes, all of which were the highest recorded of any player in the match.
Xhaka has remained on Wearside for another season and looks set to be vital once more for Sunderland's campaign ahead.
Malick Yalcouye (Brighton) - 8.6
Brighton were on the wrong end of a 4-3 defeat to Chelsea at the weekend, but they will be pleased with the performance of 20-year-old midfielder Yalcouye.
The Ivoirian was central to lots of what the Seagulls did going forward and got on the scoresheet when his powerful strike cannoned in off the post.
Yalcouye continued to be a positive influence with four successful dribbles, one key pass and one big chance created.
Morgan Rogers (Chelsea) - 8.3
Rogers was at his creative best in Chelsea's win over Brighton, earning an 8.3 Flashscore rating after providing the assist for Pedro Neto's goal.
The England international kept up his influence with four key passes and two big chances created - while also providing defensively with one tackle, three recoveries and four duels won.
Forwards
Joao Pedro (Chelsea) - 8.6
Chelsea's Brazilian star Joao Pedro was heavily involved throughout their clash with Brighton.
The striker managed to get on the scoresheet with a cool finish not long after missing from just a few yards out, before then turning provider with an assist for Cole Palmer's winner in the second half.
Joao Pedro even scored an own goal, which brings his rating down slightly alongside one big chance missed.
Erling Haaland (Manchester City) - 8.5
Haaland opened his account for the Premier League season with two goals in Manchester City's win over Crystal Palace.
The Norwegian first found the net with a superb header, before finishing off the match with a powerful effort from close range to seal all three points.
What makes his performance all the more impressive is the fact that Haaland had just six touches in the opposition box - but made them count with two vital goals.
Rayan Cherki (Manchester City) - 9.2
The star of City's win on Friday night was undoubtedly mercurial playmaker Cherki.
The midfielder earned a 9.2 Flashscore rating after scoring two goals, creating one big chance and completing three key passes.
His potential was on full show for his first goal specifically, darting past several challenges in the box before poking home to complete a lovely move.
