City were on top right from kick-off with Sterling and Aguero proving hard to handle for the Southampton defence; and just five minutes in, had taken the lead.
Manchester City cruised to victory over a sorry Southampton side to return to the top of the Premier League.
Sterling, 23, has now been directly involved in 39 Premier League goals since the start of last season, only Mohamed Salah (50) has been involved in more.
He has scored six times in nine games in 2018-19, having scored 10 in his first season under Guardiola (2016-17). I have the feeling he is now enjoying scoring goals and making assists and be important in winning games.
Aguero passed to Silva, who fed Leroy Sane out wide.
Although fulsome in his praise of the maturing centre-back pairing Aymeric Laporte and John Stones, Guardiola's defensive philosophy is dependent on a team effort to keep the ball as far away from City's goal as possible.
David Silva's through ball appeared to be going out of play but Aguero showed impressive persistence to chase and pull it back for Sterling who, first miskicked but then shot past Saints goalkeeper Alex McCarthy from six yards.
The hosts were guilty of taking their foot off the gas in the second half, and it could have been game on again as James Ward-Prowse and Ings both had attempts kept out by Ederson - the latter nodding a corner downward to force the Brazilian into a fine stop down low.
Hazard took a free kick on the right and the ball eluded several players before reaching the unmarked Morata at the back post, and he struck his fourth goal in his last four league games.
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