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 bounced back from defeat against QPR
FA Cup holders Chelsea came from a goal down against Southampton to progress to the fourth round of this year's competition.
Rafa Benitez's men fell behind midway through the first half when Jay Rodriguez beat Ross Turnbull, but were soon on level terms through Demba Ba’s debut goal.
Just before the break Victor Moses put the visitors ahead and then, soon after it, goals from Branislav Ivanovic and a second for Ba confirmed the victory, before a late Frank Lampard penalty rounded off a comfortable win.
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 Adkins, 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 who opened the scoring with a decisive breakaway. Jack Cork's ball forward fell to Jason Puncheon, who found Rodriguez with a superb first-time through ball - the striker finishing calmly with the Blues' defence nowhere to be seen.
Hazard curled narrowly wide soon after as the visitors came back, but it was not long before they were level. Moses' back-heel sliced open Saints' defence before Mata lifted the ball over Artur Boruc. The ball was already on its way into the goal but Ba was determined and pipped Steven Davis to the ball on the goalline.
And then, right on the stroke of half-time, with Benitez's men buoyed and the Saints deflated, Ashley Cole found Moses in a crowded penalty box to slot past Boruc and put the Blues ahead.
Chelsea pushed on after the break, Mata again the conductor at the heart of the Blues' midfield. 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, in turn, spotted the former Newcastle striker’s dart into the area to help him beat Boruc with ease.
A fantastic double save by Blues' keeper Ross Turnbull denied Saints from pulling a goal back, the shot-stopper first blocking Steve De Ridder’ goal-bound strike before he got up quickly to parry a Davis effort. Then, down the other end, only the feet of hosts' keeper Boruc stopped Ba from heading in for a debut hat-trick.
There was time for one more Chelsea goal late on, as Lampard came off the bench to win and convert a penalty to bag the Blues' fifth, becoming the club’s joint-second all-time goalscorer in the process. Ba will perhaps feel aggrieved he was not allowed the spot kick to try and bag a third. Nevertheless, it is the holders who progress to the next stage.