Manchester United's false dawn and Arsenal dream: Premier League talking points
But victories for the title contenders came in contrasting fashion as Arsenal blew away Newcastle 4-1, while City edged out a nervy 1-0 win at Bournemouth.
Behind the top three, it was Aston Villa's weekend in the battle for the top four.
Unai Emery's men opened up a five-point gap over Tottenham thanks to a 4-2 win over Nottingham Forest, while Manchester United's recent fine form ended abruptly in a 2-1 home defeat to Fulham.
AFP Sports looks at three talking points from the Premier League weekend.
Another Man Utd false dawn
Completion of Jim Ratcliffe's purchase of a minority stake in United, allied to a run of four consecutive league wins, meant there was an air of optimism around Old Trafford before kick-off.
Ratcliffe this week revealed his ambition to usurp Liverpool and City within three years.
But the work that lies ahead of the British billionaire was laid bare in a shambolic performance as Fulham claimed their first win at Old Trafford since 2003.
Erik ten Hag's men were barely deserving of Harry Maguire's late equaliser to cancel out Calvin Bassey's opener for the visitors.
And in their determination to push for a winner, United were caught out as Alex Iwobi finished a clinical Fulham counter-attack.
Ratcliffe also underlined the need for Champions League football next season to give United more freedom to invest without breaching financial fair play limits.
However, defeat leaves the Red Devils eight points adrift of fourth-placed Villa and with a daunting trip to City to come next weekend.
Luiz 'lifted' by Emery
Douglas Luiz has been one of the cornerstones of Villa's rapid rise under Unai Emery.
The Brazilian struck twice against Forest to take his tally for the season to nine in the Premier League, all of which have come at Villa Park.
Only Mohamed Salah has scored more home Premier League goals this season and the former Manchester City man credited Emery for developing him into an all-round midfielder.
"I just think he has lifted me, it is the truth," said Luiz. "He has told me every day, you need to defend, and if you go, you need to score."
Arsenal 'living the dream'
As Liverpool battle a mounting injury list and City struggle to find their top form, Arsenal are the form horse in the title race.
Newcastle were the latest lambs to the slaughter when faced with Mikel Arteta's free-scoring Gunners, who have struck 25 goals in six consecutive Premier League wins.
Arsenal ran out of gas down the final straight in last season's title race having led for the most of the season.
A year on and Arteta's more mature side appear to be relishing the role of chasers despite the calibre of the Liverpool and City teams ahead of them.
"We are living the dream," said captain Martin Odegaard.
"We have all dreamed of being here. You see every week how competitive it is and that is where we want to be - we want to fight for trophies."