Chelsea saw their own 100% start ended with a goalless draw against London rivals West Ham United on Saturday, with that result leaving them third behind Manchester City, who thrashed Cardiff City 5-0 in South Wales.
There was also a big win for Burnley, who finally picked up their first victory of the campaign in style against Bournemouth to lift themselves out of the relegation zone, and Leicester City have two representatives in this week's team following their 3-1 win over Huddersfield Town.
Arsenal's Petr Cech has faced serious scrutiny over his status as a top goalkeeper over the past year or so, but he was back to his best against Everton, making six saves en route to his first clean sheet of the season.
While Cech is coming towards the end of his Premier League career, one player who looks increasingly likely to have a bright future in the division is Crystal Palace's Aaron Wan-Bissaka, who once again produced a performance beyond his 20 years during the goalless draw with Newcastle. The likes of Kyle Walker, Trent Alexander-Arnold and Pablo Zabaleta deserve honourable mentions, but Wan Bissaka gets the nod on the right this week.
Ben Chilwell is the first of three Leicester players in this week's team following his display in the win over Huddersfield, earning his place ahead of the likes of Danny Rose and Fabian Delph on the left flank.
At the heart of the defence, Liverpool's Joel Matip offered a reminder to Jurgen Klopp about his quality with a goal and a clean sheet on his first start of the season, while James Tarkowski was every bit as impressive for Burnley as the attackers at the other end.
There is plenty of competition for midfield places in this week's team, but we cannot overlook the Man City midfield duo of Bernardo Silva and Ilkay Gundogan, both of whom registered a goal and an assist in the rout of Cardiff.
Crystal Palace's Luka Milivojevic completed more tackles and dribbles and saw more of the ball than any other player in their draw with Newcastle, which is just about enough for him to beat the likes of Jorginho, Declan Rice and Ruben Neves into the team. Fred, Johann Berg Gudmundsson and Joao Moutinho are among the other honourable mentions in midfield.
The Man City theme continues up front with Raheem Sterling's assist earning him a place alongside Burnley's Aaron Lennon, who helped himself to a goal and an assist in the win over Bournemouth.
Two-goal Riyad Mahrez also deserves a mention, and there were as many as six players competing for the central striking role, including Sergio Aguero, Alexandre Lacazette, Aleksandar Mitrovic, Kelechi Iheanacho and Ashley Barnes.
However, the nod goes to Jamie Vardy this week, with the Leicester striker registering a goal and an assist at the King Power Stadium.