However there was never a hint that Southampton might be able to launch anything resembling a fightback and City ended the half as they had begun it - by scoring.
The last time the two sides met at the Etihad, City had a golden opportunity to win the league, but they gave away a two-goal lead to lose 2-3.
It was proving a nightmare return for Southampton manager Mark Hughes, who was in charge at City during 2008-09, as his side conceded a third when Sterling supplied a cross and David Silva lashed the ball home. Kevin de Bruyne and Claudio Bravo are long-term absentees while Eliaquim Mangala is not yet match-fit.
Guardiola confirmed that both Ilkay Gundogan and Nicolas Otamendi are available after recovering from knocks.
He said: "Every game is important".
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"We have a chance to step into next round, then we have three or four days to think about Manchester United [on Sunday]".
Whereas some English clubs, most notably when Liverpool play at Anfield, treat European nights with special reverence, City remain largely ambivalent and there will once again be a below capacity crowd for the match against Ukraine champions Shakhtar Doentsk on Wednesday night.
Ivan Ordets, Maksym Malyshev and Fernando all look unlikely to feature for the visitors due to injury.
Southampton got a little encouragement when Danny Ings was brought down by City keeper Ederson and rose to convert the spot kick in the 30th minute but on the stroke of half-time City restored their three-goal advantage when Aguero passed to Sterling inside the box and he took his time before firing home.
Meanwhile, Saints are now seven Premier League games without a victory and lie 16th. Of course Manchester United is a big game but we can not start thinking about that until we have played Shakhtar.
So far City's failure to land Jorginho, who instead choose to follow Maurizio Sarri in the move from Napoli to Chelsea in July, to share the burden as the midfield anchor hasn't proved costly.
Shakhtar Donetsk faced 24 shots in their 0-3 defeat to Man City on MD3, the most they'd faced in a Champions League game since September 2015 against Real Madrid (26). They create two versus ones in good areas.