A Rickie Lambert penalty cancelled out Yaya Toure's early goal from the spot, but late strikes by Samir Nasri and Edin Dzeko meant the 2011-12 champions went into the break with a two-goal lead, an advantage they extended through Stevan Jovetic with nine minutes left.
The result vaulted City above Chelsea and just one point behind leaders Liverpool.
However, City will still have two games in hand over their rivals after their matches. Chelsea meet Stoke later on Saturday and Liverpool will play West Ham on Sunday.
The loss left Southampton, who drew 1-1 with City earlier in the season, in eighth place on 48 points.
Worse, the Saints lost England striker Jay Rodriguez, who was carried off on a stretcher with a knee injury midway through the first half after landing badly as he jumped to control the ball.
Manuel Pellegrini's men have made the Etihad a fortress this season, winning 14 of their 15 League matches on home soil.
The solitary defeat came against Chelsea in February, but City's response has been to take 17 points from seven League fixtures since then.