Tammy Abraham scored his eighth goal for Chelsea before Mason Mount looked to set the visitors on their way.
Danny Ings would pull one back on the half-hour mark to give Southampton a glimmer of hope, but N’Golo Kante quelled any chance of a comeback when he restored Chelsea’s two-goal advantage five minutes from halftime and Michy Batshuayi added a fourth after the break.
Southampton has claimed just seven points from their first eight matches to start the year and are without a point in the last three.
Angus Gunn has conceded nine goals since his last clean sheet, which came in the win over Sheffield United, giving manager Ralph Hasenhuttl more to think about with Alex McCarthy an option in goal.
Southampton: Gunn, Bertrand, Yoshida, Bednarek, Valery, Hojbjerg, Romeu, Ward-Prowse, Long (Obafemi 73), Ings (Adams 81), Redmond (Boufal 81)
Unused subs: McCarthy, Stephens, Armstrong, Danso
Goals: Ings (30)
Chelsea: Arrizabalaga, Alonso, Tomori, Zouma, Azpilicueta, Jorginho, Kante, Hudson-Odoi (Pulisic 80), Mount (Kovacic 80), Willian, Abraham (Batshuayi 84)
Unused subs: Caballero, Barkley, Christensen, James
Goals: Abraham (17), Mount (24), Kante (40), Batshuayi (89)
Bookings: Jorginho (12)