The Saints started the game strongly and took the lead through Jay Rodriguez who fired home from the edge of the area after 22 minutes.
The goal only lifted the away side though, and they equalised on 35 minutes, as Ba marked his debut with a goal, tapping in from close range following good work from Eden Hazard.
Chelsea continued to push and went ahead just before half-time with Victor Moses firing home after Ashley Cole has raided down the left.
The game carried on in very much the same vein in the second half and Rafa Benitez's men made the perfect start as Branislav Ivanovic headed home from the close range.
The Blues just kept coming, regularly exposing Southampton's defensive problems, before Ba doubled his tally, with Hazard once again providing the assist before Frank Lampard rounded off the scoring from the penalty spot after 83 minutes.