Victory saw City close to within a point of Liverpool with a game in hand and leapfrog Chelsea into second place.
But Chelsea, who've also played one game more than City, will go a point clear at the top if they beat Stoke at Stamford Bridge in Saturday's late kick-off.
Liverpool are away to West Ham on Sunday.
Everton and Arsenal, fifth and fourth respectively before the weekend, clash at Goodison Park on Sunday.
The opening four goals at Eastlands all came in the first half with City's Yaya Toure and Saints' Rickie Lambert both scoring from the penalty spot before Samir Nasri and Edin Dzeko scored in stoppage-time to make it 3-1 to Manuel Pellegrini's men.
City substitute Stevan Jovetic completed the scoring nine minutes from time.
"I haven't seen it (City's second goal) yet but it is the referee who decides," City manager Manuel Pellegrini told Sky Sports.
"I don't think the difference between the two sides was just one goal.
"Southampton played very well in the first half with lots of possession. We didn't play well in the first half but we scored three goals and had two clear chances to score.
"Now we have an important game against Liverpool. We shall see what happens, there is a lot of time to prepare. I don't think that game will decide the Premier League.
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