The champions had slipped down to third place following shock losses to Crystal Palace and Leicester City, but they returned to winning ways in comfortable fashion on the south coast to move back above Tottenham Hotspur into second place.
City did have to survive a brief scare after Pierre-Emile Hojbjerg had cancelled out David Silva's opener, but a quickfire brace at the end of the first half - including an own goal from James Ward-Prowse and a header from Sergio Aguero - enabled them to cruise through the second half.
Southampton ended the match with 10 men courtesy of a late red card for Hojbjerg, but it had no impact on the result as City moved to within seven points of leaders Liverpool ahead of next Thursday's mouth-watering showdown between the top two at the Etihad Stadium.
Pep Guardiola responded to his side's dip in form by making five changes to his starting XI - including returns for Silva and Fernandinho in midfield - while Southampton also rang the changes with six new faces, including a daunting Premier League debut for 18-year-old Kayne Ramsay.
It took only five minutes for the champions to create their first chance as Jack Stephens was caught in possession inside his own area by Raheem Sterling, who in turn teed up Silva to be denied by a fine save from Alex McCarthy.
Southampton had a clear sight of goal themselves in the opening exchanges when Charlie Austin was sent clean through by Mohamed Elyounoussi, but his first touch let him down and Ederson was able to collect the ball.
It proved to be a costly wasted moment for the home side as Man City broke the deadlock just 65 seconds later, when Riyad Mahrez and Bernardo Silva combined to set up the fit-again David Silva, who swept home a simple finish from inside the area.
The champions had thrown away leads in each of their previous three matches prior to today, but they initially showed no signs of suffering the same fate this afternoon as they dominated the opening half-hour.
Mahrez almost produced a goal of the season contender as City passed the ball around inside their own box before hitting Southampton on the break, with the Algerian carrying it from the halfway line to the edge of the box only to fire his finish wide when he should have at least hit the target.
Another slick passing move almost created a second goal in the 25th minute, but Southampton once again had McCarthy to thank for keeping the score down when he pulled off a brilliant save to deny Aguero from Sterling's low cross.
The hosts had struggled to get out of their own half up to that point, but they began to grow into the game around the half-hour mark and Ederson only narrowly escaped the attentions of Ward-Prowse inside his own six-yard box before showcasing his shot-stopping ability with a smart save to deny Austin's flicked header from a corner.
Southampton's improvement gave them the belief and confidence to start closing City down, though, and they reaped the rewards eight minutes before half time when Hojbjerg caught Oleksandr Zinchenko in possession before blasting his finish past a helpless Ederson from just inside the area.
That was only the start of the drama at the end of the first half, though, and a revitalised Southampton felt that they should have had a penalty with two minutes until the break when Ward-Prowse went down under the challenge of Zinchenko.
Referee Paul Tierney waved the claims away, and less than two minutes later Ward-Prowse was bemoaning another stroke of bad luck as he inadvertently diverted Sterling's low cross past McCarthy, who could not react quickly enough to keep the ball out at the near post.
It was a hammer blow for Southampton just as they appeared to be getting on top, and worse was to come in stoppage time of the first half as Aguero ghosted in between two defenders to plant a downward header from Zinchenko's cross past McCarthy.
Hojbjerg drew a routine save from Ederson in the opening stages of the second half, but the action-packed end of the first appeared to have taken the wind out of Southampton's sails and they never really looked like hauling themselves back into the game for a second time.
McCarthy may have done better for both goals at the end of the first half, but he also prevented Southampton from losing by a much larger margin with further saves in the second half - one of which he made with his head to deny Sterling.
The Saints also needed the woodwork to come to their rescue when Aguero clipped the top of the crossbar with a shot on the turn, and the striker was also denied by a sliding block at the back post shortly after the hour mark.
Sterling saw a penalty appeal turned down moments later as City went in search of a fourth goal without ever really getting out of second gear, and Mahrez should have provided it 10 minutes from time only to fire straight at the keeper after being released by Gabriel Jesus.
Hojbjerg then saw a dipping volley routinely collected by Ederson, but the midfielder's afternoon ended prematurely when he was shown a straight red card for a crunching challenge on Fernandinho.
The result leaves Southampton only outside the relegation zone on goal difference courtesy of Burnley's victory over West Ham United, with the Saints falling to consecutive home defeats for the first time since September 2017.
Man City, meanwhile, leapfrog Spurs into second and could now close the gap on Liverpool to four points when they host the league leaders in their first match of 2019.
SOUTHAMPTON (4-3-2-1): McCarthy; Ramsay, Stephens, Bednarek, Targett; Hojbjerg, Lemina (Redmond 46'), Romeu (Valery 59'); Ward-Prowse, Elyounoussi; Austin (Long 68')
MAN CITY (4-3-3): Ederson; Danilo, Kompany, Laporte, Zinchenko; Bernardo, Fernandinho (Walker 86'), Silva; Mahrez (Sane 84'), Aguero (Jesus 73'), Sterling