The Gunners briefly claimed top spot after recording two successive wins at the start of a season for the first time in 10 years when they battled past Burnley on Saturday, only to be knocked off the summit by Liverpool's narrow triumph over Southampton later that day.
Champions Manchester City dropped points in dramatic circumstances as they were denied a late winner by VAR in their 2-2 draw with Tottenham Hotspur, while Manchester United were also made to share the spoils by Wolverhampton Wanderers on Monday night.
Frank Lampard is still searching for his first win as Chelsea boss after they were held by Leicester City - one of four draws from the 10 fixtures as Brighton & Hove Albion and West Ham United also played out a stalemate.
The promoted teams generally fared better as Sheffield United and Norwich City both picked up their first wins since returning to the top flight, although Aston Villa are still pointless after losing at home to Bournemouth.
Here, Sports Mole selects its Premier League team of the week for gameweek two.
Hugo Lloris may have conceded twice at the Etihad, but things would have been a lot worse for Spurs without their captain, who made eight saves in the draw as his goal was peppered with shots. Jordan Pickford and Dean Henderson also deserve mentions for being the only two keepers to register a clean sheet this weekend.
With Everton and Sheffield United claiming those rare clean sheets it is unsurprising to see them make up three of the back four. Yerry Mina was a large reason behind the Toffees' continuation of their fine defensive record at home of late, while Lucas Digne also played his part and had an impact going forward too, providing the assist for the only goal of the game.
One of the stories of the weekend was Sheffield United's first home win in the top flight for 12 years, and while goalscorer John Lundstram made himself the hero, Jack O'Connell was every bit as important to the historic success.
On the right, Ricardo Pereira earns his place having helped Leicester to turn things around in the second half against Chelsea, making eight tackles in the process to keep Christian Pulisic's threat down to a minimum.
For a second week in a row we have indulged ourselves with an attacking midfield, and while the holding duo of Kevin De Bruyne and Dani Ceballos may not be your archetypal destroyers, they would certainly provide a lot of creativity from deep.
Ceballos is already well on his way to becoming a fan favourite at the Emirates following a dream full debut which not only saw him chalk up two assists, but also create more chances, have more touches and attempt more passes than any other Arsenal player - not to mention run further than anyone else on the park before his withdrawal.
De Bruyne also helped himself to a couple of assists to well and truly announce himself as back to his best after an injury-plagued 2018-19 campaign, leading to comparisons with Premier League legends such as Steven Gerrard and David Beckham.
Sadio Mane was the main man for Liverpool at Southampton on what proved in the end to be a nervy victory, breaking the deadline in sublime fashion against the run of play before providing the assist for Roberto Firmino to bag what proved to be the winner.
There was plenty of competition for the midfield spots, with Ruben Neves considered in a holding role following his stunner against United, Manuel Lanzini in the conversation and Erik Lamela, Mason Mount and Bernard all pushing for inclusion having got themselves on the scoresheet.
The number 10 role in this week's team goes to James Maddison, though, after he grabbed the game by the scruff of the neck to lead Leicester to a point at Stamford Bridge. The 22-year-old may have been guilty of missing a golden chance to win it, but he did provide a pinpoint assist for the opener and was head and shoulders above anyone else on the park in the second half.
Todd Cantwell makes it a pair of young English attacking midfielders in the XI having announced himself on the big stage with two assists during Norwich's 3-1 win over Newcastle United, although even he had to play second fiddle to the star of that particular show.
Teemu Pukki's sensational hat-trick made him the first name on this week's team sheet and, with four goals in his first two games of the season, will no doubt have Fantasy Football managers scrabbling to sign him up.body check tags ::