After Chelsea continued their 100 percent start with a 3-0 win over Burnley on Saturday, a last-gasp goal by Marcus Rashford helped Jose Mourinho keep pace with his old club as Manchester United beat Hull City 1-0.
Elsewhere, Arsenal and champions Leicester City picked up their first Premier League wins of the season by beating Watford and Swansea City respectively while Tottenham Hotspur came from behind to draw 1-1 at home to Liverpool.
New manager Antonio Conte has promised to restore Chelsea's belief after they finished 10th last season and goals from Eden Hazard, Willian and Victor Moses secured top spot in the table after a one-sided encounter at Stamford Bridge.
Then, in the late game of the day, United joined the Londoners on nine points when they sank Hull thanks to a stoppage-time effort by substitute Rashford.
Hazard, a crushing disappointment under former manager Mourinho last season, again showed he was back to his best this term with a brilliant solo goal in the ninth minute against Burnley.
The Belgium winger also played a part in the second goal by Brazil midfielder Willian before substitute Moses rounded off a sweeping late Chelsea move.
"The team played very well, created a lot of chances," Conte said. "To keep a clean sheet is very important to increase our confidence in the work we are doing."
United were frustrated in wet conditions by Hull's dogged defending before the 18-year-old Rashford struck by converting Wayne Rooney's cross.
"We did everything to win," said Mourinho. "When you score at 90-something you always talk about luck but the fact is we deserved it.
"We were so intense in our attacking ways, I always believed the goal would arrive."
World record signing Paul Pogba was shackled by the home side's disciplined midfield but he did go close with a thunderous late shot.
"We frustrated them at times and we contributed to the game by going forward," said Hull boss Mike Phelan as his side saw their 100 percent record ended by his former club United.
First-half goals by Santi Cazorla (penalty), Alexis Sanchez and Mesut Ozil gave Arsenal a 3-1 win at Watford to ease the pressure on manager Arsene Wenger.
"We had a good cushion at halftime," Wenger said. "At the moment we're not completely there physically and you could see that in the second half."
Debutant Roberto Pereyra pulled one back for Watford with an unstoppable drive.
Leicester got back to winning ways after Jamie Vardy's trademark strike and Wes Morgan's second-half goal downed Swansea 2-1 at a rainswept King Power Stadium.
Vardy beat keeper Lukasz Fabianski after being picked out by Danny Drinkwater before captain Morgan slammed home from close range.
Leroy Fer replied for Swansea late on after Leicester's Riyad Mahrez had a 56th-minute penalty saved by Fabianski.
Manager Juergen Klopp was left frustrated at Tottenham as Liverpool failed to kill the game despite their early dominance.
James Milner converted a 43rd-minute penalty for the visitors after Erik Lamela had fouled Roberto Firmino but Philippe Coutinho and Sadio Mane were denied during a one-sided first half.
Danny Rose made Liverpool pay for their profligacy with a 72nd-minute equaliser.
"We must be more clinical," Klopp said. "When you take a point at Tottenham for 99 percent of teams it would be a good thing but today we saw the game differently."
Everton continued their unbeaten start when they overcame Stoke City 1-0 thanks to keeper Shay Given's own goal while Southampton and Crystal Palace grabbed late equalisers to earn 1-1 draws with Sunderland and Bournemouth respectively.