The home side then sealed the victory with 10 minutes left on the clock as substitute Stevan Jovetic tapped in from close range.
Here, Sports Mole takes a closer look at the action between the two sides.
On target: 8
On target: 1
Was the result fair?
While the scoreline may have flattered Manchester City in the end, there can be no denying that the hosts deserved to come away with the points. The Blues struggled for large parts of the opening 45 minutes, but they were able to control the contest once they scored those two quick goals in first-half stoppage time.
Man City's performance
Manuel Pellegrini's side were well below par for the first 30-odd minutes of the game as they failed to live with Southampton's dynamic approach. The Blues struggled to hold onto the ball and did not inspire when they tried to go forward. However, scoring two goals at the end of the first half seemed to take the weight of expectation off their shoulders. They looked like a different team in the second half, keeping the visitors at arm's length with some probing and incisive attacking play that was more reminiscent of the City that has lit up the Premier League for most of the season.
The Saints took the game to their hosts early on and fully deserved to get back on terms when Rickie Lambert levelled things up from the penalty spot. The visitors looked to be enjoying themselves during the first half as they carved City open multiple times thanks to some fearless football. It was only in the dying minutes of the half that they lost control, conceding two quick goals to give themselves a mountain to climb. After that they never really posed a threat to the home side. Had they been more clinical in the final third when they were on top then there could very well have been a different outcome to this match.
Sports Mole's man of the match
David Silva: The Spaniard was at the centre of all of Manchester City's attacks, linking play superbly with some intricate passing while creating space for teammates thanks to his excellent positioning and movement.
Edin Dzeko was guilty of a shocking miss just before Southampton equalised, somehow heading the ball over from close range following Pablo Zabaleta's cross to the back post. The striker may have got on the scoresheet later on, but this was not one of his better days in a City shirt.
It was a busy afternoon for Chris Foy. The official was correct in awarding the two penalties, even though City's may have been a soft one. However, he is sure to come under fire for the home side's second goal as David Silva looked about four yards offside before setting up Samir Nasri. Foy may have needed a bit of help from his linesman, but this was a poor decision whichever way you look at it.
Man City: The Blues are back in Premier League action next Sunday when they make the crucial trip to Anfield to face title rivals Liverpool.
Southampton: The Saints continue their Premier League campaign next Saturday at home to strugglers Cardiff City.