London clubs' erratic start to the Premier League season improved with victories for Chelsea, Tottenham Hotspur and Arsenal but Manchester sides continued to make the running, with United and City leading the way on 10 points each.
United surrendered their 100 per cent record in a lively 2-2 draw at Stoke City after Pep Guardiola's City had trounced 10-man Liverpool 5-0 to replace their neighbours at the top for a few hours.
Stoke took the lead just before halftime through Cameroon international Eric Maxim Choupo-Moting, then conceded an equaliser less than three minutes later, as Nemanja Matic flicked on a corner and Paul Pogba's header hit Marcus Rashford and went in.
Romelu Lukaku put United ahead in the 58th minute, only for Choupo-Moting to equalise.
City benefited from the dismissal of Sadio Mane before halftime as they inflicted Liverpool's heaviest defeat since Juergen Klopp took over almost two years ago.
The Senegalese forward was adjudged guilty of endangering an opponent by catching Brazilian goalkeeper Ederson in the face with a high foot.
Already trailing to a Sergio Aguero goal, Liverpool conceded two more to Gabriel Jesus on either side of halftime and fell to a rare five-goal defeat when Leroy Sane also scored twice in the final quarter of an hour.
Ederson was taken off on a stretcher but suffered no break and tweeted later that he was fine.
Chelsea had a 2-1 win away to Leicester in the meeting of the previous two seasons' champions.
N'Golo Kante scored against his former club soon after halftime to extend Chelsea's lead after Alvaro Morata claimed his third goal in four league games since moving from Real Madrid.
Leicester, having made two changes at the interval, halved the deficit with a Jamie Vardy penalty but the champions held on to move into third place.
Tottenham's Harry Kane reached 100 goals for the club with a freak opening effort in the comfortable 3-0 win at Everton, adding a second later.
After the home side started brightly, the England striker deceived goalkeeper Jordan Pickford from way out on the right wing just before the half-hour. "I got a lucky one but sometimes you need that," Kane said.
Christian Eriksen scored the second after Pickford made a good save from Ben Davies and Kane knocked in Davies' pass a minute after the interval.
The win pushed Spurs into the top five and provided a boost ahead of their opening Champions League game against Borussia Dortmund at Wembley, where they are playing home league games this season but have yet to win one.
Their north London rivals Arsenal, heavily criticised after defeats by Stoke City and Liverpool, were easy winners at home to struggling Bournemouth, prevailing 3-0.
Danny Welbeck gave them the lead and close-season signing Alexandre Lacazette doubled it before halftime. After Jermain Defoe headed against a post Arsenal broke out for Welbeck to claim his second.
Bournemouth were pushed into the bottom two on goal difference by their fourth successive defeat.
Promoted Brighton, back in the top tier for the first time since 1983, achieved their first win, by 3-1, at home to West Bromwich Albion.
New signing Pascal Gross scored twice and Tomer Hemed added the third before a consolation by James Morrison, giving West Brom a first defeat.
In the day's other game unbeaten Watford moved above Southampton and into the top four by beating them 2-0 with goals by Abdoulaye Doucoure and substitute Daryl Janmaat.