Liverpool showed their credentials in targeting a first title since 1990 are for real and such was the Reds' dominance the scoreline did not do Jurgen Klopp's men justice in winning 2-1 at Tottenham.
Chelsea also made it five wins from as many games under Maurizio Sarri thanks to the brilliance of Eden Hazard, who scored a hat-trick in a convincing 4-1 win over Cardiff to edge ahead of Liverpool on goal difference.
City remain just two points back and looked back to their best in tearing apart Fulham 3-0 thanks to goals from Leroy Sane, David Silva and Raheem Sterling.
Liverpool's first win away at Tottenham in four attempts for Klopp was another sign of the progress made under the German, particularly as they suffered a 4-1 thrashing at Wembley last season.
"Nobody will play the perfect season. It's still early, five games, fantastic we won all five and improved. I like that development," said Klopp.
"Now we have to prove that and do it again and again."
Spurs paid a heavy price for the absence of captain Hugo Lloris through injury as stand-in goalkeeper Michel Vorm flapped at a corner six minutes before the break and Georginio Wijnaldum looped a header over the line before Vorm could scramble clear.
Roberto Firmino tapped home a second nine minutes into the second-half and Liverpool should have added to their lead as Sadio Mane and Naby Keita were denied by Vorm.
However, the visitors had to see out a nervy final few seconds when Erik Lamela skillfully volleyed home from a narrow angle and Son Heung-min had a penalty appeal waived away with the final attack of the game.
Sane returns in style
City and Chelsea await in Liverpool's next three league games and remained in touch with the leaders with comfortable home victories.
Pep Guardiola started Leroy Sane for the first time this campaign and last season's Premier League Young Player of the Year looked more like his old self as Fulham were put to the sword.
Sane tapped home Fernandinho's inviting cross inside two minutes before Silva smashed his 50th Premier League goal and Sterling completed the rout.
Sarri is still to taste anything but victory in English football, but had a scare early on at home to Cardiff when Sol Bamba put the visitors in front at Stamford Bridge.
However, Cardiff's failure to significantly strengthen over the summer means they are liable to being outclassed at this level and were undone by the brilliance of Hazard.
The diminutive Belgian scored twice in seven minutes to send Chelsea in ahead at half-time and completed his hat-trick from the penalty spot before Willian added a fourth.
Mesut Ozil quietened his critics with his first goal since February as Arsenal continued to creep up the table with a 2-1 win at Newcastle.
The Gunners are still not firing on all cylinders under new boss Unai Emery, but Granit Xhaka's free-kick put them on course for a third straight win before Ozil compounded Newcastle's misery as the Magpies remain rooted in the bottom three.
Bournemouth moved up to fifth with an impressive 4-2 victory over 10-man Leicester with Ryan Fraser scoring twice.
And Wilfried Zaha underlined his importance to Crystal Palace with the only goal in his return from injury in a 1-0 win at Huddersfield.