On an incident-packed day of goals, red cards and drama in England's top flight, Chelsea preserved its five-point lead — and its unbeaten start to the campaign — by beating Crystal Palace 2-1 thanks to a free kick from Oscar and a great team goal finished off by Cesc Fabregas.
Second-placed City is leading the chase, with Aguero grabbing two goals in each half — two coming from penalties — and also missing from the spot in a 4-1 win over 10-man Spurs. The champions have now scored 15 goals in three straight wins over Tottenham.
Southampton stayed a point behind in third after scoring five times in the final 27 minutes against imploding Sunderland, narrowly missing out on equaling the record margin of victory in the Premier League held by Manchester United from its 9-0 win over Ipswich in 1995.
"I'm still a little bit in shock," Southampton manager Ronald Koeman said. "Sometimes football is strange."
Danny Welbeck's stoppage-time strike secured injury-hit Arsenal a 2-2 draw at home with Hull, and goals by Phil Jagielka, Romelu Lukaku and Seamus Coleman earned Everton a 3-0 win over Aston Villa.
West Ham's surprising start to the season continued with a 3-1 win at Burnley, lifting the London team provisionally into fourth place.
Newcastle eased some pressure on manager Alan Pardew by beating Leicester 1-0 in a match whose kickoff was delayed by an hour after part of a newly erected big screen was dislodged by wind at St. James' Park.
Some 28 goals were scored in seven matches and almost a third was netted by Southampton, which recorded the fourth 8-0 win in Premier League history.
The Saints were expected to struggle this season after selling a number of top players over the summer like Adam Lallana, Luke Shaw and Rickie Lambert.
But the south-coast club is surprising everyone — including Sunderland, which virtually gave up in an embarrassing second-half effort.
"It's probably the most embarrassing time I've had on a football pitch," Sunderland manager Gus Poyet said. "You think that maybe you will never get these situations, but unfortunately sometimes it's your turn. It's unacceptable really."
Sunderland scored two own goals — one a volley from just inside his own area by Santiago Vergini — while Graziano Pelle struck twice to take his haul for the season to seven goals and there were other goals from Jack Cork, Dusan Tadic, Victor Wanyama and Sadio Mane.
That victory — Southampton's biggest in the Premier League — upstaged Aguero's effervescent attacking display against Spurs, with his four goals moving him level with Chelsea striker Diego Costa as the Premier League's top scorer with nine.
"I think he demonstrated why people say he is one of the best strikers in the world," City manager Manuel Pellegrini said after a game that featured four penalties and a red card.
Aguero opened the scoring in the 13th with a low drive and restored City's lead from the penalty spot in the 20th after Christian Eriksen had equalized.
City goalkeeper Joe Hart saved a penalty from Roberto Soldado in the 62nd before Aguero scored in the 68th — from the spot after Federico Fazio was red-carded for pulling back the striker — and the 75th.
The huge wins for City and Southampton couldn't reduce their deficit to Chelsea, whose seventh win in eight games came without the injured Costa and in a match where both teams finished with 10 men.
Oscar put the visitors ahead in the sixth minute with an exquisite free kick from 30 yards out before Chelsea had Cesar Azpilicueta sent off in the 40th for a two-footed challenge on Mile Jedinak. Within a minute, though, Palace also lost a player as defender Damien Delaney was given a second booking after bringing down Loic Remy.
Fabregas added the second in the 51st with his first league goal in Chelsea colours, before Frazier Campbell netted a 90th-minute consolation.
"My team had a fantastic performance," Chelsea manager Jose Mourinho said. "From minute one, we did what we wanted to do, have the ball, use the ball and control the game. After that comes the red cards. And 10 against 10, with the qualities we have, was even easier for us."