The 3-1 victory has lifted City above Tottenham Hotspur, shock 3-1 losers to Wolves Saturday, into second place in the standings but still seven points adrift of Liverpool.
The top two face off at the Etihad Stadium Thursday in a match which looks key to the eventual destination of the title and with leader Liverpool in top form after its 5-1 demolition of fifth-placed Arsenal in its latest fixture of the crowded Christmas program.
"We wanted to bounce back and we did it brilliantly today," said City manager Pep Guardiola, relieved after a run of three defeats in four EPL matches.
But he is warning his players they can't afford to make any mistakes against Liverpool if they want stay in the title hunt.
"With the position of Liverpool, if we drop points then it is over, it is finished, it would be almost impossible," he told reporters.
"Of course they are going to drop points, but not too many," he added in a frank assessment.
Any thoughts Guardiola's side might be suffering a hangover from damaging successive losses to Crystal Palace and Leicester, were put to rest by an early goal from David Silva after a cutback from Bernardo Silva on 10 minutes.
More might have followed as Southampton was pinned back in its own half, but a mistake by Ukrainian Oleksandr Zinchenko led to an equalizer eight minutes before the break.
Zinchenko, replacing Fabian Delph in the problematic left-back slot for City, was caught in possession and Pierre-Emile Hojbjerg charged forward to poke home a strong shot past Ederson in the visiting goal.
Appeals for a home penalty after James Ward-Prowse went down under challenge from the shaky Zinchenko were waved away as Southampton enjoyed its best spell, but it proved short lived.
Raheem Sterling charged in on goal from the left and his effort was deflected past Alex McCarthy by the unfortunate Ward-Prowse.
On the stroke of halftime, Zinchenko made amends for his earlier error with an accurate cross for Sergio Aguero to head his 14th goal of the season to make it 3-1.
There was no further scoring in the second half, despite the continuous attacking threat of Sterling, with Aguero striking the crossbar with an effort before being substituted with Thursday's match in mind.
With five minutes left, Hojbjerg blotted his copybook with a heavy challenge on Fernandinho, whose welcome return to the City side coincided with its return to form.
"Speak with any club in the world and they all have important players and Fernandinho is one for us," said Guardiola.
The Danish international was shown straight red, leaving Southampton down to 10 men for the final moments, its recent revival under new manager Ralph Hassenhuttl halted by the reigning champion.
Earlier Sunday, Chelsea kept pace with the leading trio with a narrow 1-0 victory at struggling Crystal Palace.
N'Golo Kante scored the only goal of the match after 51 minutes as he latched on to a through ball from David Luiz.
Chelsea, which stays fourth, two points adrift of Tottenham, also hit the woodwork twice in a match it controlled against a team that has mustered just five goals at home all season in the Premier League.
At the other end of the table, there was some relief for Burnley, with a 2-0 home win over West Ham to draw level on points with Southampton but still in the bottom three.
Pogba double lifts resurgent United
In Sunday's late kickoff, Manchester United continued its revival under new caretaker manager Ole Gunnar Solskjaer as Paul Pogba scored twice for the second straight game in the 4-1 home win over Bournemouth.
The French World Cup star did the damage in the first half with fifth and 33rd minute strikes to put United firmly in command, its grip on the game tightening when the excellent Marcus Rashford scored the third just before halftime.
But there was just time for Nathan Ake to head a Bournemouth reply before the break and keep his side in the match.
Pogba continued his excellent play in the second period, coming close to a hat-trick as he rattled the woodwork and setting up substitute Romelu Lukaku for United's fourth.
A late sending off for United defender Eric Bailly for a reckless challenge on Ryan Fraser could not spoil the afternoon for Solskjaer with his team winning three straight and scoring 12 goals since he took over.
Pogba believes United has a more attacking mindset under Solskjaer than previous boss Jose Mourinho.
"We are more offensive and creating more chances and that is how we want to play," he said.