The win takes the Blues up to fifth on the table with 14 points from eight games played.
Tammy Abraham and Mason Mount were again on the scoresheet for Chelsea, as were N’golo Kante and substitute Michy Batshuayi, rendering Danny Ings’ strike a mere consolation in the end.
The hosts started on the front foot with Nathan Redmond hitting a powerful strike from 20 yards just over the Chelsea bar in the opening minute.
For all of Southampton’s early endeavor, it was Chelsea who took the lead in the 17th minute after Tammy Abraham clipped Callum Hudson-Odoi’s long pass over Southampton goalkeeper Angus Gunn, with the ball just crossing the line despite Maya Yoshida’s best efforts to clear.
Seven minutes later, the visitors went two up through another of their academy graduates; Mason Mount this time blasting the ball past Gunn after he was fed by Willian.
Southampton halved the deficit on the hour mark when Danny Ings turned in Jan Valery’s low cross but N’golo Kante restored the visitors’ two-goal lead just ten minutes later after the Frenchman’s effort from outside the box deflected off Saints captain Pierre-Emile Hojbjerg and wrong-footed Gunn into the net.
Hudson-Odoi missed a great chance to score his first Premier League goal as Gunn came out on top in a one-on-one situation eight minutes after the restart.
Chelsea put the result beyond doubt a minute to full time after substitutes Michy Batshuayi and Christian Pulisic combined beautifully, allowing the Belgian to slot the ball past Gunn for a comprehensive victory for Frank Lampard’s men.