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.
However, controversy surrounded Nasri's goal that made it 2-1 with David Silva, who played in the French midfielder, in an offside position when he received the ball only for referee Chris Foy and his linesmen to let play continue.
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.
"I don't remember (City goalkeeper) Joe Hart making an important save. They had possession but no real 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."
Defeat was made worse for Southampton by a first-half injury suffered by Jay Rodriguez, one of their England strikers, that placed a huge question mark against his chances of making into Roy Hodgson's squad for this June's World Cup finals in Brazil.
Rodriguez landed badly after jumping to control the ball in the 26th minute and clutched his knee in agony before being carried off on a stretcher.
"I don't know how Jay Rodriguez is. It's not looking good but we'll be assessing it in Southampton," said Saints boss Mauricio Pochettino, who was furious at the decision to let Nasri's goal stand.
"This action from the linesman for the second goal killed the game, the linesman killed the game," he said.
"It's clear that the second goal changed it. We were superior up that point, we can analyse the game to that point but there is no point after that. It just killed off the game."
Saturday's other matches see Manchester United, buoyed by their midweek Champions League draw with Bayern Munich, away to struggling Newcastle while bottom of the table Fulham travel to Aston Villa.