Aguero peels away after equalising for Man City
Edin Dzeko scored within a minute of coming off the bench to give Manchester City a dramatic late win over Fulham, while Liverpool hammered Norwich 5-2.
The Cottagers took an early lead when Pablo Zabaleta was adjudged to have fouled John Arne Riise in the area and Mladen Petric slammed home the penalty.
Fulham keeper Mark Schwarzer made a series of fine saves before Sergio Aguero levelled from close range.
And City were unable to turn pressure into chances before a Gael Clichy cross fell for Dzeko in the 87th minute.
And at Goodison Park, two goals by Nikica Jelavic continued Everton's flying start to the season as David Moyes's side came from behind to seal a fourth win in six league games and push them second on the table.
Record £12m signing Gaston Ramirez gave Southampton the lead at Goodison with a header from Adam Lallana's corner.
But Leon Osman levelled from eight yards after a cross by Kevin Mirallas, who then threaded a pass for Croatian striker Jelavic to make it 2-1.
Jelavic cemented victory with a header after good work by Seamus Coleman.
Everton's flying start
This is Everton's best start to a Premier League season after six games since the 2004-05 campaign - when they finished fourth
While Southampton have now conceded an alarming 18 goals in six Premier League games, Everton's latest success adds weight to the belief that Moyes's men can challenge for Champions League qualification.
The hosts displayed great character to recover from a desperate start to score all three goals in the space of 13 first-half minutes and leave the Saints longing for the half-time whistle.
On the eve of the match, Moyes, in the final year of his Goodison Park contract, ruled out imminent discussions to resolve his long-term future, the Scot insisting he was more concerned with concentrating on his team's healthy start than sorting out his own future.
And Luis Suarez scored a hat-trick as he led Liverpool to a first Premier League win of the season at Norwich.
Suarez drilled in a strike from the edge of the box before stroking in a second following a defensive mistake.
The Uruguayan set up Nuri Sahin for a tap-in and Suarez curled in shot for his hat-trick before Steve Morison drove in an effort for the home side.
Steven Gerrard's deflected strike added Liverpool's fifth, while Grant Holt angled in a shot for a late home goal.
In other matches Reading played 2-2 with Newcastle, Stoke beat Swansea 2-0 and Sunderland beat Wigan 1-0.