Erling Haaland slammed the ball into the roof of the Southampton net after just five minutes, but despite a host of chances, Pep Guardiola's side could not add to the score, reports Xinhua.
The win lifts City two points clear of Liverpool and six ahead of Arsenal, who are fourth after Aston Villa and Bournemouth drew 1-1.
Villa looked as if they were on for all three points when substitute Ross Barkley put them ahead in the 76th minute, but Evanilson salvaged a point for the visitors at the very end with a header into the corner of the net.
There were also late goals as Brighton and Wolverhampton Wanderers drew 2-2 in one of two top-flight thrillers.
Danny Welbeck's sixth goal of the season put Brighton ahead in the stroke of halftime and the three points looked as if they were staying at home when Evan Ferguson doubled the lead with just five minutes left to play.
Rayan Ait-Nouri fired home for Wolves in the 88th minute after a corner, and Matheus Cunha finished a counter-attack with a finish into the top-corner in the third minute of injury time.
Ipswich Town suffered late heartbreak in a 4-3 defeat away to Brentford in a chaotic game.
Sam Szmodics and George Hirst put Ipswich 2-0 up after half an hour, but two goals in two minutes on the stroke of halftime from Yoane Wissa and Harry Clarke, who couldn't keep a Wissa shot out of the net, helped Brentford level the score.
Bryan Mbeumo put Brentford ahead from the penalty spot and Clarke was sent off to leave Ipswich with 10 men, but Liam Delap still leveled for the visitors.
Mbeumo scored the winner in the 96th minute with a cross that evaded everyone, but there was still time for Delap to hit the crossbar to almost salvage a point for Ipswich.
Everton substitute Beto netted a close-range header deep into injury time at home to Fulham, when it looked as if a 61st-minute effort from former Everton midfielder Alex Iwobi was going to secure all three points for the visitors.
Beto's late goal extends Everton's unbeaten run to five games and lifts them six points clear of the bottom three.
On Friday, Nottingham Forest striker Chris Wood continued his excellent start to the season with two goals as his side won 3-1 away to Leicester City.
Ryan Yates opened the scoring for Forest, with Wood's goals coming in the second half after Jamie Vardy had canceled out Yates' opener.
The result is a blow for Leicester coach Steve Cooper, who is a popular figure with Forest after his years with the club.
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