It had looked as though the Oriol Romeu's 75th minute equaliser had slowed the City juggernaut, but Sterling curled an unstoppable effort past Fraser Forster at the death to send the Etihad Stadium crowd wild.
Sterling has now scored the winning goal in three successive games for City.
City were never at their fluent best but Kevin De Bruyne's free kick, which took a touch off of Saints defender Virgil van Dijk, put them ahead straight after halftime.
Forster made some crucial saves to keep his side in the game and former Chelsea player Romeu struck with a shot off the underside of the crossbar to reward Southampton who had gone close twice before the break.
Sterling's moment of brilliance ensured that City stayed on course to break Arsenal's all-time record winning streak in the Premier League and restored their eight-point lead over Manchester United who won at Watford on Tuesday.
(Reporting by Martyn Herman; Editing by Toby Davis)
