Sterling then bagged a couple of his own after Danny Ings had pulled one back for the visitors from the penalty spot, before Leroy Sane capped another fine afternoon for the champions with an edge-of-the-box shot into the bottom corner.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ederson; Walker, Stones, Laporte, Mendy; Bernardo, Fernandinho, D.Silva; Sane, Aguero, Sterling
SUBS: Muric, Danilo, Kompany, Delph, Mahrez, Jesus, Foden
STARTING XI: McCarthy; Soares, Stephens, Hoedt, Bertrand; Redmond, Ward-Prowse, Hojbjerg, Lemina; Long, Ings
SUBS: Gunn, Yoshida, Vestergaard, Austin, Elyounoussi, Armstrong, Obafemi
Pep Guardiola: "I am impressed with the quality Southampton have in the middle and at the front. They have huge talent and are so deep and so physical. It is so complicated to beat them. We must be sharp and move well and be clever. It will be a tough game."
Mark Hughes: "There are always elements of any team that you can look to exploit, no matter how good they are. City get into winning positions very quickly which we can't let happen. They are going to have a lot of possession and we need to be patient and know when to press and when we can't press."
MANCHESTER CITY SUBS: Muric, Danilo, Kompany, Delph, Mahrez, Jesus, Foden
SOUTHAMPTON SUBS: Gunn, Yoshida, Vestergaard, Austin, Elyounoussi, Armstrong, Obafemi