The Senegal international was denied the chance of a hat trick when Frank Lampard took and scored a late penalty, as Rafa Benitez's men bounce back from defeat against QPR
Rafa Benitez's men bell behind midway in the first-half when Jay Rodriguez beat Ross Turnbull in a one-on-one, but were soon on level terms through a debut goal from Demba Ba.
Just before the break Victor Moses but the visitors ahead and then, soon after, goals from Branislav Ivanovic and a second for Ba confirmed the victory, before a late Frank Lampard penalty put the icing on the cup-cake.
The result will go some way towards making up for a poor defeat at the hands of Premier League bottom-boys QPR on Wednesday.
Ba made his first start for the Blues in one of five changes from the defeat to QPR. Ashley Cole, Eden Hazard, Juan Mata and Ramires also returning in a strong line-up. Nigel Akins, meanwhile, rested Rickie Lambert and Gaston Ramirez, bringing in James Ward-Prowse and Jay Rodriguez in his two changes from the Arsenal draw.
After a subdued opening 20 minutes it was the home side that opened the scoring with a decisive breakaway. Jack Cork's venture forward was cut-out but the ball fell to Jason Puncheon who found Rodriguez with a superb first-time through ball, the striker finishing calmly with the Blues' defense nowhere to be seen.
Hazard curled narrowly wide soon after as the visitors came back, but it wasn't long before they were level. Victor Moses, Hazard and Mata were involved in the build-up before Mata lifted the ball over Artur Boruc. The ball was already on its way but Ba was determined to open his Chelsea account, and did so by pipping Steven David to the ball right on the goal-line.
And then, right on the stroke of halftime, with Rafa Benitez's men buoyed and the Saints deflated, Ashley Cole found Moses in a crowed penalty box with the Nigeria international's effort finding its way past Boruc to put the Blues ahead.
Chelsea then pushed on after the break, Mata again the conductor at the heart of the Blues' attack. The Spain international worked himself some space on the left flank with some nice play, before crossing for Ivanovic to head home.
A fourth soon followed and it was Ba who doubled his tally. Ramires started the move by finding Hazard, who then sent a cross into the path of the former Newcastle man who had no trouble in beating Boruc.
A fantastic double save by Blues' keeper Ross Turnbull denied Saints from pulling a goal back, the stopper firstly blocking a Steve De Ridder strike when he looked certain to score before he got up quickly to again save from Steven Davis. Then, at the other end, only the feet of Boruc stopped Ba from heading in for a debut hat trick.
There was time for one more Chelsea goal late on, Frank Lampard coming off the bench to win and take a penalty to bag the Blues' fifth, becoming the joint-second all-time goalscorer at the west London club. Ba will perhaps feel aggrieved he wasn't allowed the kick to try and bag his debut hat trick. Nevertheless it is Chelsea which moves on to the next stage.