Pep Guardiola's champions needed to regain their footing after stumbling against Crystal Palace and Leicester, and did so with strikes from David Silva, Sergio Aguero and James Ward-Prowse's own goal at St. Mary's.
Charlie Austin should have put Southampton ahead but miscontrolled the ball after being played in on goal and City immediately took advantage, with Bernardo Silva teeing up David Silva to slot home unmarked in the 10th minute.
Alex McCarthy made a good save to keep out Aguero from point-blank range after good work by Sterling and City were made to pay for their profligacy when Pierre-Emile Hojbjerg slammed home after robbing Oleksandr Zinchenko.
City regained the lead when Sterling's cut-back deflected against Ward-Prowse and in after 45 minutes and Aguero headed home another from Zinchenko's cross in the third minute of first-half stoppage time.
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McCarthy made good saves to deny Sterling and Mahrez after the break, while Aguero hit the crossbar and Hojbjerg was sent off for a rash tackle on Fernandinho.
City's Brazilian defensive midfielder returned to the side after missing three matches with a thigh injury and added security in the City defence but missed chances, particularly from Mahrez, prevented them from adding to their tally.
"We missed a lot of chances, (it could have been) 6-1, 7-1, we had to score. Liverpool are not going to give us that amount of chances," warned Guardiola.
"We had 30 exceptional minutes, made chances, we conceded a goal and when Saints were at their best we scored our second one. It's amazing in terms of the result, in terms of the play.
"Unfortunately we lost two (matches) and our next opponent is one of the top teams in Europe."
Defeat left Southampton 17th in the table on 15 points, the same as 18th placed Burnley, who beat West Ham United 2-0 on Sunday.
With the scores level at 1-1 Southampton appealed for a penalty after Ward-Prowse tumbled in the area following pressure from Zinchenko, but referee Paul Tierney correctly waved away their claims.
City, who had suffered three league defeats in four matches, might have wobbled again had it been given but regained composure to sweep to a comfortable victory.
(Writing by Rik Sharma; Editing by Ian Chadband)
