With second-placed Manchester United settling for a drab stalemate at Anfield earlier in the day, it was their Manchester rivals who provided the thrills as City moved two points clear at the top.
Capping a dramatic day, Arsenal trail nine points behind City after Watford came from behind to snatch a surprise 2-1 win.
Pep Guardiola's free-scoring City struck three times in the first 27 minutes at Eastlands, securing their sixth successive league win in swashbuckling style yesterday.
David Silva got City's third with a simple finish after another incisive raid in the 27th minute.
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Stoke's Mame Biram Diouf reduced the deficit with a deflected effort in the 44th minute and City's defence was breached for just the fourth time in the league this season when Kyle Walker scored an own goal two minutes after the interval.
But Jesus's second goal in the 55th minute restored order and his compatriot Fernandinho put the result beyond doubt five minutes later.
Bernando Silva's first City strike, in the 78th minute, made it 24 goals in his team's last five league games.
They are the first team to net 29 goals in the first eight games of an English top-flight campaign since Everton in 1894-95 and Guardiola said: "We can always do better but I cannot deny today was the best performance since I arrived here.
"I am here to win, I am not here to entertain, but this is the way we want to play. Our confidence is high."
But stunningly it was Chelsea who were the victims as they finally ended that goal drought at Selhurst Park.
Palace took the lead in the 11th minute when Yohan Cabaye's effort was deflected in for an own goal by Chelsea defender Cesar Azpilicueta.
Tiemoue Bakayoko equalised for Chelsea seven minutes later as the France midfielder headed his first Premier League goal from a Cesc Fabregas corner.
However, Chelsea were already without injured duo Alvaro Morata and N'Golo Kante and they suffered another setback when Victor Moses limped off in the first half.
- Infuriated -
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Chelsea were condemned to a second successive league defeat after their damaging 1-0 loss to Manchester City before the international break.
Antonio Conte's side, beaten three times this term, are now nine points behind City.
"The performance level today was not up to the standard it should be. We played poorly," Chelsea captain Gary Cahill said.
At Vicarage Road, injury-plagued defender Per Mertesacker headed Arsenal in front in the 38th minute with his first Premier League goal since December 2013.
That set the stage for Tom Cleverley to fire home in stoppage-time as Watford, who climb to fourth place, handed Arsenal their first loss in eight games in all competitions.
"It was a scandalous decision, but what can we do? Nothing. You can talk and talk but at the end of the day they scored," Wenger said of the controversial penalty.
At Anfield, Liverpool manager Jurgen Klopp was left infuriated by United boss Jose Mourinho's ultra-cautious game-plan.
Mourinho's team had just six touches in Liverpool's penalty area as United goalkeeper David De Gea made a superb save from Joel Matip to maintain the visitors' unbeaten start to the season.
"I think Man United came here for the point and they got it," Klopp moaned.
"I'm sure if we played like this, you could not do this at Liverpool. Obviously for Man United it is OK."
Inevitably, Mourinho had no regrets, saying: "The second half was a bit of chess, but my opponent didn't open the door for me to win the game."
Tottenham finally won for the first time at Wembley in the Premier League with a 1-0 victory over Bournemouth thanks to Christian Eriksen's deft 47th-minute finish.
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