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That was his 13th goal of the season and moved City onto a record 40 points from the first 14 games. For Sterling, though, three is always the magic number.
The winger said: "They made it really difficult for us but we have a feeling in the dressing room that nobody wants to drop points.
"We know that the teams behind us are pushing hard. United were brilliant last night.
"The only records we are interested in are three points in the next game: West Ham."
City had gone ahead through Kevin De Bruyne's deflected free-kick just after the break, but the stubborn Saints hit back through Oriol Romeu.
It looked like the visitors' game plan had worked until Sterling somehow found space just outside a jam-packed penalty area to fashion a shot into the top corner.
Cue pandemonium at the Etihad Stadium, and another memorable night in a thrilling season so far.
Man City team news ahead of the game with Southampton