What you need to know:
- Liverpool had a brief taste of life at the top, beating Wolves 3-1 in the early kick-off before City took pole position.
- In-form Tottenham scored two goals in stoppage-time to beat Sheffield United 2-1.
Manchester United's crisis deepened on Saturday as they slumped to a 3-1 home defeat against Brighton, while Manchester City beat West Ham to stay perfect on a day of heart-stopping drama in the Premier League.
Liverpool had a brief taste of life at the top, beating Wolves 3-1 in the early kick-off before City took pole position.
In-form Tottenham scored two goals in stoppage-time to beat Sheffield United 2-1.
The season is spiralling out of control for Erik ten Hag's United, who started the campaign in buoyant mood after ending their trophy drought and finishing third in the league last season.
Some fans dreamed of a long-overdue title challenge but instead they find themselves trailing leaders City by nine points after a third chastening defeat in five matches.
United started brightly at Old Trafford, desperate to put their nightmare start to the season behind them but their former forward Danny Welbeck silenced the home fans in the 20th minute.
A 53rd-minute goal by Pascal Gross gave United a mountain to climb and substitute Joao Pedro made it 3-0, with Hannibal Mejbri's first United goal little consolation for the shell-shocked hosts.
Brighton's fourth straight league win against United lifted them to third in the table.
A disappointed Ten Hag said it was a game of "small margins".
"We conceded a goal with their first attack," he told Sky Sports. "We then had a period in the game that was quite difficult, we fought to get a goal and it was disallowed.
"So it is difficult in this period. It has not fallen on our side, but we will fight back and if we stick together, play as a team, stick to the rules, we will return."
Ten Hag, in his second season at Old Trafford, faces a huge job to save United's season, besieged by problems on and off the pitch.
Jadon Sancho has been exiled from first-team training after a public spat with the manager, while fellow forward Antony has been given a leave of absence to address domestic abuse allegations, which he denies.
Protests continue in the stands against unpopular owners the Glazer family, who appear to have put their attempt to sell the club on hold.
Champions Manchester City, two points clear of Liverpool, continue to churn out the wins, even though Pep Guardiola's men trailed to a first-half James Ward-Prowse goal at the London Stadium.
Jeremy Doku equalised early in the second period and Bernardo Silva put City 2-1 up before Erling Haaland's seventh goal of the season guaranteed a fifth win in five games.
Sheffield United looked to be on track for their first league victory of the season at the Tottenham Hotspur Stadium.
But Spurs grabbed an equaliser in the 98th minute when Richarlison headed home Ivan Perisic's corner and Dejan Kulusevski scored the winner.
Earlier, Jurgen Klopp's Liverpool roused themselves after an anaemic first-half display against Wolves, recovering from a goal down.
Cody Gakpo scored 10 minutes into the second period and Andy Robertson finished neatly in the 85th minute before an own goal from Hugo Bueno added gloss to the scoreline.
It was the third time this season that Liverpool had come from behind to win.
Klopp said his team deserved to win the game after their powerful second-half performance but stressed that they could not afford to keep falling behind.
"Turning games around is helpful in a season but we cannot rely on it," he told the BBC.
"We have to play better in the first half of games generally. We are not stable yet, that is not possible. Too many things are new."
Aston Villa scored three late goals to beat Crystal Palace 3-1.
The London side led 1-0 courtesy of Odsonne Edouard's first-half goal but Jhon Duran equalised in the 87th minute.
Douglas Luiz scored a penalty deep into stoppage time to put Villa in front and Leon Bailey made it 3-1.
Fulham's Carlos Vinicius condemned Premier League new boys Luton to a fourth consecutive defeat as the Cottagers won 1-0.
Struggling Newcastle host Brentford in the evening kick-off.