Hoedt’s own goal gave City a sixth-minute lead, the centre-back – whose initial failed clearance brought about the move – finding his own net when attempting to keep Sane’s shot out.
Aguero doubled their tally from close range after Sterling breezed through Saints’ hapless defence and passed into the danger zone.
Sterling was integral again for the third, with his cross nudged on by Sane, and Silva smashed home on the volley.
Ings’ penalty – after Ederson hauled him down – saw Saints pull one back, but Sterling restored the three-goal cushion just before the interval, slotting home after tireless work from Aguero.
But City still looked in control and they got a fifth just past the hour – Sterling drilling under Alex McCarthy after Aguero fed him into the area.
Sane completed the rout with a sixth in the closing minutes, picking out the bottom-left corner from the edge of the box after being found on the break by Sterling.