The Blues are a rejuvenated side under Maurizio Sarri and two men inspired by the new manager this term were influential on Sunday, with Ross Barkley creating Eden Hazard's opener and netting the second himself to open his account for the visitors, before the Belgium star teed up a third for Alvaro Morata.
Barkley was on the very fringes of Antonio Conte's Chelsea team, in which the system shackled star performer Hazard, but the pair are thriving now and combined to devastating effect at St Mary's.
Although Southampton had chances to make the three points a trickier conquest for the visitors, Sarri's men were deserving winners as they sent a message to their closest title rivals.
Desperate early attempts to crowd out Hazard saw a loose ball break to Willian for a deflected shot that looped onto the crossbar, before Southampton belatedly responded and Danny Ings somehow volleyed over the top from four yards.
Wesley Hoedt was fortunate not to concede a penalty as he slid into Olivier Giroud and the hosts' luck then ran out when Barkley freed Hazard to calmly send the goalkeeper the wrong way.
Another big Saints miss followed the restart as Ryan Bertrand lashed off target and they again paid the price, with the unmarked Barkley stabbing into the net from a misdirected Giroud scissor-kick.
A late flurry saw Nathan Redmond rattle the crossbar and Morata then shoot straight at Alex McCarthy on the counter, before the Chelsea forward made amends with a dinked finish in the third minute of stoppage time.