City, who had trounced Manchester United 6-3 last week, barely had to break stride against Southampton, with Joao Cancelo, Phil Foden and Riyad Mahrez netting before Erling Haaland struck the fourth goal to stretch his scoring streak to 10 straight matches in all competitions.
The victory took champions City top of the table with 23 points after nine matches and cranked up the pressure on early title rivals Arsenal, who host Liverpool on Sunday with the chance to reclaim the lead. Former Chelsea forward Diego Costa made his first start for the visitors but Potter's side were dominant and secured a third consecutive win in all competitions thanks to goals from Kai Havertz, Christian Pulisic and Armando Broja, moving up to fourth in the table on 16 points.
Bruno Guimaraes, a 40-million-pound arrival from Olympique Lyonnais and one of the club's biggest signings since the takeover, scored in each half on a memorable afternoon for the club, who were languishing in the relegation zone when the Saudi Public Investment Fund acquired the club from previous owner Mike Ashley for a reported 300 million pounds .