Liverpool moved up to second in the table, while Brighton & Hove Albion leapfrogged Tottenham Hotspur and Arsenal into third place on Sunday afternoon.
Chelsea, meanwhile, lost at home to Aston Villa after being reduced to 10 men and remain with only one win under Mauricio Pochettino in the Premier League.
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See: What happened in the north London derby
Liverpool extend unbeaten run
Liverpool extended their unbeaten run to 17 Premier League matches, dating back to April, with a 3-1 win over West Ham United.
West Ham started the match better at Anfield but were unable to score from Tomas Soucek and Michail Antonio headers.
Liverpool made them pay on 16 minutes, when Mohamed Salah won and converted a penalty. It made Salah the fifth player to either score or assist in each of his team's first six matches of a Premier League season, after David Beckham for Manchester United in 2000/01, Thierry Henry for Arsenal in 2004/05, Sergio Aguero for Manchester City in 2019/20 and Erling Haaland for Man City in 2022/23.
West Ham were back on level terms three minutes before half-time, Jarrod Bowen heading home Vladimir Coufal's cross to maintain his record of scoring in every away Premier League match his season.
Liverpool went back ahead on 60 minutes. A clever dinked ball over the West Ham defence from Alexis Mac Allister found Darwin Nunez, who applied a first-time finish for his third league goal of the campaign.
With five minutes remaining, Diogo Jota converted a knockdown from Virgil van Dijk, as Liverpool made it five straight wins to move on to 16 points, just two behind early leaders Man City.
A 19th match at Liverpool without a win as a manager for David Moyes leaves his side in seventh on 10 points.
Mitoma at the double
Substitute Kaoru Mitoma scored twice as Brighton came from behind to win 3-1 against AFC Bournemouth.
Dominic Solanke gave Bournemouth the lead on 25 minutes, lifting a left-footed effort over goalkeeper Bart Verbruggen, who was off his line having been caught out trying play out from the back.
Brighton were level in first-half added time. A free-kick from Billy Gilmour was turned into his own net by Cherries defender Milos Kerkez.
Roberto De Zerbi brought on Mitoma at half-time and the Japanese scored just 16 seconds after the restart. He exchanged passes with Mahmoud Dahoud before finishing into the far corner from inside the box.
Mitoma wrapped up the win on 77 minutes with a close-range header from Pervis Estupinan's third assist of the season.
It means Bournemouth remain without a win and are 17th, with three points.
Watkins strikes as Chelsea's struggles continue
Ollie Watkins scored his first Premier League goal of the season as Aston Villa condemned 10-man Chelsea to a 1-0 defeat at Stamford Bridge.
Reaction from the head coach. 💬#CheAvl pic.twitter.com/AkafMWCvhb
— Chelsea FC (@ChelseaFC) September 24, 2023
Chelsea had to play most of the second half without Malo Gusto, who was shown a red card for a bad tackle on Lucas Digne.
Villa made their extra man count on 73 minutes. Moussa Diaby played in Watkins, who, despite being forced wide by Levi Colwill, fired in from a narrow angle at the second attempt beyond Robert Sanchez.
Chelsea pressed for an equaliser, but it never came, as they failed to find the back of the net for a third successive league match, taking 45 shots in that time.
A third loss of the season leaves Chelsea 14th, with five points. Villa move up to sixth, with 12 points.