An own goal from Wesley Hoedt and further first-half strikes by Sergio Agüero
, David Silva and Raheem Sterling were separated by a Danny Ings penalty, before Sterling added his second after the interval and Leroy Sane rounded things off.
Mark Hughes made three changes to the side that drew 0-0 with Newcastle United, with Pierre-Emile Hojbjerg, James Ward-Prowse and Shane Long coming in, while there was a place on the bench for 18-year-old striker Michael Obafemi.
Pep Guardiola’s side went into the contest knowing victory could move them back to the top of the Premier League and two points clear of Liverpool, after Jurgen Klopp’s men drew 1-1 at Arsenal.
With that, the hosts were ahead after six minutes when Sane was played in by David Silva, and his low cross was turned into his own net by Hoedt.
Agüero was in search of his 150th Premier League goal, and just six minutes later he had it when Sterling picked up possession before driving to the byline and cutting the ball back to the Argentine for a simple finish.
It was a dominant spell that showed no signs of relenting, with City’s interchangeable movement proving hard to contain and the England international winger Sterling was again the architect for the hosts third. His cross fell loose to David Silva inside the box, and he crashed the ball home high into the net on the volley.
Saints’ first sustained spell of possession brought a chance when Cedric’s delivery from the right saw Ings make a move to the near post but he couldn’t make a telling touch.
But two minutes later, there was a lifeline for Hughes’s men when Ryan Bertrand’s ball found the run of Ings, who had got inside of John Stones, and Ederson brought him down for a penalty that the summer signing from Liverpool coolly converted.
It was imperative that Saints continued to find their feet in the contest, but instead they were punished right on the stroke of half-time when Agüero outmuscled Cedric before a low cross that allowed Sterling to fire home.
A switch to 4-4-2 was a clear attempt to force City back and it almost paid dividends early in the second-half, when Ward-Prowse’s powerful drive was fumbled by Ederson to Ings, but the Brazilian was quick to react to make amends and thwart the danger with a save.
With pressure building, those reactions were needed again when Ings flicked a near post header goalwards from Ward-Prowse’s corner, only for it to be pushed away.
But as the game became increasingly stretched, City made it five when Agüero unselfishly fed Sterling in for his second of the afternoon.
Substitute Michael Obafemi’s movement, on just his second appearance for the club, almost helped pull a goal back when he went down the right and provided a ball back for Long, who screwed his shot wide.
A break away saw it become a painful six late on when Sterling got in down the left and played a simple pass to Sane, who curled the ball behind an unsighted Alex McCarthy.
It’s Watford next up at St Mary’s, and a result is imperative for them if they want to avoid dropping into the dreaded relegation zone.