Wesley Hoedt gifted City, who needed little help, an opening goal before Sergio Aguero — his 150th in the Premier League — and David Silva tallied to make it 3-0 inside 20 minutes.
Danny Ings ended Southampton’s five-match Premier League goal drought from the penalty spot, but any glimmer of an unrealistic comeback was dispelled when Raheem Sterling made it 4-1 on the stroke of half-time.
Sterling, again, and Leroy Sane each scored after the break against a despondent and lifeless Saints, who remains 16th in the table, with Newcastle nipping at their heels and the bottom three just two points away.
Manchester City: Ederson, Walker, Stones (Kompany 72), Laporte, Mendy, Fenandinho (Delph 79), Silva (Foden 72), Sane, Sterling, Bernardo, Aguero.
Unused subs: Muric (GK), Danilo, Mahrez, Jesus.
Goals: Hoedt (OG 6), Silva (18), Aguero (12), Sterling (45+2, 67), Sane (90+1).
Bookings: Aguero (38).
Southampton: McCarthy, Bertrand, Hoedt, Stephens, Cedric, Lemina, Hojbjerg, Ward-Prowse (Obafemi 73), Redmond (Elyounoussi 73), Ings, Long.
Unused subs: Gunn (GK), Yoshida, Vestergaard, Armstrong, Austin.
Goals: Ings (PEN 30).
Bookings: Ward-Prowse (10).