Chelsea ended Southampton’s five-game Premier League unbeaten run.
Eden Hazard and Diego Costa scored either side of the break for high-flying Chelsea.
Southampton last suffered a defeat in the league at Arsenal in September, but remain in ninth place in the standings after 10 games.
Thibaut Courtois has kept four-straight league clean sheets for the Blues, who have collected maximum points in that stretch.
An in-form Hazard gave the visitors the lead with six minutes gone when he wrong-footed Steven Davis along the byline before smashing a shot through Fraser Forster’s.
Charlie Austin had a chance to bring Southampton level in the 14th minute, but turned his header from Steven Davis’ free-kick well wide of the upright.
Southampton dominated possession after falling behind, though they didn’t register their first shot on target until the 29th minute when Dusan Tadic’s low free-kick was saved by Courtois.
Hazard looking to add to his opening tally flashed a curling shot on target from outside the box on 38 minutes, only for the angle to be covered by Forster.
With Chelsea content to soak up pressure and hit back on the counter, Nemanja Matic picked off a poor pass in the midfield before finding Diego Costa in space, whose right-footed effort from in close was saved four minutes from halftime.
Jose Fonte provided a vital clearance of Marcos Alonso’s cross to prevent Hazard from having a tap-in chance shortly after the restart.
But Diego Costa doubled the lead with a sensational curling strike that beat Forster to the far corner in the 55th minute.
Chelsea nearly added a third off the rebound of Victor Moses’ effort, but Southampton recovered to prevent any shot on goal.
Steven David saw his header deflect off David Luiz and over the bar 15 minutes from full-time, as Southampton looked for a consolation goal against a clinical opposition.
Charlie Austin thought he'd brought the Saints back within one with a late goal, but he was ruled offside.
Southampton: Forster, Bertrand (McQueen 88), van Dijk, Fonte (c), Martina Romeu, Clasie (Boufal 61), Davis, Redmond, Tadic (Hojbjerg 78), Austin.
Unused subs: Taylor (GK), Yoshida, Ward-Prowse, Olomola.
Chelsea: Courtois, Azpilicueta, David Luiz, Cahill (c), Moses (Ivanovic 87), Kante, Matic, Alonso, Pedro (Willian 77), Diego Costa (Batshuayi 88), Hazard.
Unused subs: Begovic (GK), Terry, Chalobah, Oscar.
Goals: Hazard (6), Diego Costa (55).