Everton, who won their first four league games and drew their fifth against Liverpool last weekend, stayed top of the standings. However, only goal difference separates Everton from Liverpool.
Klopp now only has two fit senior centre-backs in Joe Gomez and Joel Matip, with midfielder Fabinho providing impressive cover in the midweek Champions League victory over Ajax
Premier League: 'To say it was pre-meditated is not fair', Carlo Ancelotti defends Pickford over Van Dijk horror tackle
Pickford has come in for heavy criticism after his challenge in last week's Merseyside derby, which left the Dutch defender with knee ligament damage.
Liverpool fuming at 'stupid' Jordan Pickford challenge on Virgil van Dijk that requires ACL knee surgery
Pickford will not face any retrospective punishment after referee Michael Oliver took no action on the field, nor was he instructed to review in the incident by VAR.
Premier League: Liverpool must stay in trophy hunt for injured Virgil van Dijk, says Jordan Henderson
Liverpool face their first challenge without Van Dijk in Wednesday's Champions League group match away at Dutch side Ajax.
Premier League: Liverpool will wait for Virgil van Dijk like a good wife for a jailed husband, says Jurgen Klopp
Van Dijk was on the end of a shocking challenge from Everton goalkeeper Jordan Pickford in Saturday's 2-2 draw in the Merseyside derby
Premier League: Liverpool defender Virgil van Dijk to undergo surgery on right knee, could miss months of action
Van Dijk was the subject of a reckless lunge by Everton's Pickford in the sixth minute of the 2-2 draw at Goodison Park on Saturday.
After the match, Liverpool manager Klopp said: "I saw back the Henderson goal and I didn't see offside. The picture I saw is no offside, but it was offside because somebody decided it."
City returned to winning ways after an indifferent start to the season, courtesy of a first-half goal from Raheem Sterling, who condemned Arsenal to their seventh straight defeat in league matches between the two sides.
Liverpool has been placed under the "very high" alert level of the British government's new three-tier system to check the spread of Covid-19.
Premier League: Everton's Dominic Calvert-Lewin credits Carlo Ancelotti's influence as key factor behind England call-up
Calvert-Lewin has scored nine goals already this season, including two hat-tricks, as the Toffees have soared to the top of the Premier League table and progressed to the quarter-finals of the League Cup.
Godfrey made 30 appearances for relegated Norwich in the Premier League last season, and had been linked with a number of top-flight clubs during transfer window.
Everton will head into the Merseyside derby against Liverpool after the international break with maximum points from their first four games.
Matchday previews: Marcelo Bielsa's Leeds host Manchester City; Roma seek first win of season against Udinese
Roma seek their first win of the season when they visit Udinese, who lost their opening two matches.
League Cup: Manchester City, United breeze past Burnley, Brighton to reach quarter-finals; Everton also advance
Guardiola's men would have won by an even bigger scoreline but for a fine display from Burnley keeper Bailey Peacock-Farrell.
Premier League: Chelsea come back from dead to draw at West Brom; Manchester United snatch 100th-minute win
It is Everton who are setting the early pace in the Premier League as they secured a third straight win in controversial circumstances, 2-1 at Crystal Palace.
League Cup: Hat-trick for Kai Havertz as Chelsea stroll past Barnsley; wins for Arsenal, Newcastle, Everton
Kai Havertz — signed for $92 million — announced himself in English football by scoring a first career hat-trick in Chelsea's 6-0 win over Barnsley in the third round of the League Cup
Premier League: Wilfried Zaha nets brace as Crystal Palace stun Manchester United; Arsenal edge West Ham
It was a chastening start to the season for United, who have come under fire from fans frustrated at their relatively modest transfer outlay compared to their title rivals.
League Cup: Premier League clubs Leeds, Southampton crash out of tournament; Everton thrash Salford City
Southampton boss Ralph Hassenhuttl named a strong side at St Mary's but still got no response from their disappointing start to the season at Crystal Palace on Saturday.
Premier League: Dominic Calvert-Lewin nets, James Rodriguez shines as Everton beat Tottenham; Leicester victorious
It was the first time Tottenham coach Jose Mourinho — who has previously managed Chelsea and Manchester United — has lost his opening match of a Premier League season, having been unable to sign a backup option to Kane.