Chelsea tasted defeat for the first time this season as Pep Guardiola's Manchester City earned a statement 1-0 win at Stamford Bridge on a day that Manchester United were beaten by Aston Villa and Liverpool were held by Brentford.
City ended a poor run against Thomas Tuchel's Chelsea thanks to a Gabriel Jesus goal early in the second half.
In the other early kickoff, Manchester United slumped to a first Premier League defeat of the season as they lost 1-0 to Villa with Bruno Fernandes missing a last-gasp penalty.
That paved the way for Liverpool to go top later, although Juergen Klopp's side had to be settle for a point as Brentford secured a 3-3 draw in a thriller.
Liverpool have 14 points from six games with City, Chelsea, United and Everton all on 13 points.
Brighton & Hove Albion could go top with 15 points if they beat Crystal Palace on Monday.
Tuchel had enjoyed mastery over his Man City counterpart Guardiola, winning all three matches against him since arriving at Stamford Bridge in January -- a sequence culminating in the Champions League final victory.
But this time Guardiola won the tactical battle as his side dominated possession and barely gave Chelsea, who were joint top before the lunchtime kickoff, a sniff.
Jesus's low shot on the turn in the 53rd minute earned City the win and but for Chelsea goalkeeper Edouard Mendy they would have enjoyed a bigger margin.
Victory made Guardiola City's most successful manager in terms of wins with 221 since taking charge in 2016.
"I am so proud," Guardiola said. "What we have done in these five years -- players, backroom staff and all at the club -- working together to improve the club. It's an honour.
"Hopefully we can make more (wins) and the next manager can come and break the record. It means we have won many games. It's why we have won a lot of titles."
It was a reality check for Chelsea whose cautious approach backfired completely.
"We were excellent but only in the last 20 metres of the match, not in the other 80 metres," Tuchel said.
"Part of performance is to make an opponent underperform and City did that. They were stronger, sharper, had more precision."
Villa went ahead in the 88th minute at Old Trafford thanks to a header by Kortney Hause but his handball then gave United a penalty in a frantic finish.
Fernandes stepped up but blazed over, with manager Ole Gunnar Solskjaer upset with the antics of Villa's players.
"Bruno has been such a good penalty taker," Solskjaer told reporters. "You would back him with your mortgage. What I did not like to see was the way they crowded the penalty spot and the referee to try to affect Bruno.
"It clearly worked for them but that is not great to see. They achieved what they wanted to."
Mohamed Salah scored his 100th Premier League goal for Liverpool but it was not enough to earn his side victory.
Ethan Pinnock put Brentford ahead but Diogo Jota levelled and Salah struck in the 54th minute.
Vitaly Janelt headed in a rebound to make it 2-2 and although Curtis Jones put Liverpool back in front in the 67th minute, Brentford snatched a point as substitute Yoane Wissa struck in the 82nd.
"We went toe-to-toe with one of the best teams in Europe. We have a well-earned point and were very brave throughout the game," Brentford manager Thomas Frank said.
West Ham United, who beat Manchester United in the League Cup in midweek, followed up with a 2-1 victory against Leeds United thanks to a late goal by Michail Antonio at Elland Road.
Norwich City's horrendous start to the season continued as they made it six defeats from six games with a 2-0 loss at Everton.
Jamie Vardy scored twice for Leicester City and once for Burnley in a 2-2 draw, although Burnley had a late 'winner' cancelled out by a VAR check. Watford also had a late goal disallowed by VAR as they came back to draw 1-1 at home to Newcastle United who are still without a league win.
