As Fernando Torres sat on the substitutes' bench and watched Chelsea haul themselves back into this tie, he may well have felt his humiliation was complete. It took the Spaniard 14 games, 732 minutes to be precise, to score his first goal for Chelsea after his £50m transfer from Liverpool in January 2011, and here was Demba Ba requiring just 61 minutes to get two on his debut for the club.

It was the sort of impact a striker can only dream of and could well provide Torres with a deepening of his Stamford Bridge nightmare. For the 28-year-old, having started 31 of Chelsea's 33 competitive games this season, may now have to get used to watching from the sidelines. Certainly he has stiff competition for the team's lone-striker berth with Ba putting in an impressive display following his £7m arrival from Newcastle on Friday, showing a level of muscular determination – something that has been sorely lacking in Torres's play over the past two years.

The first of his goals got Chelsea on level terms after they had fallen behind to Jay Rodriguez's opener while his second extended the FA Cup holders' lead to 4-1. Rafa Benítez, Chelsea's interim manager, insisted the pair could play together in attack but he is a man who prefers one up front and, on current form, Ba is undoubtedly the frontrunner for that role.

"I prefer this problem," said Benítez when asked it would be difficult for him to choose between Torres and Ba. "For some time we have only had one striker and it is important for the team to have these different options. They can compete or they can play together. We will see."

Ba's display was just one of the highlights of a hugely satisfactory afternoon for Chelsea, who well and truly banished the painful memories of Wednesday's shock 1-0 defeat to Queens Park Rangers with a display of ruthless attacking swagger, the seal on which was placed with a Frank Lampard penalty on 83 minutes that enabled the midfielder, who came on as a 65th minute substitute, to go level with Kerry Dixon as Chelsea's second all-time record scorer with 193 goals, nine behind Bobby Tambling. Little wonder those packed into the away end could be heard chanting: "Sign him up," soon after the 34-year-old had placed the ball past Artur Boruc in the Southampton goal.

"It is a great achievement for Frank and hopefully he can score more goals until the end of the season," Benítez said before he was then asked to respond to claims that Lampard's agent was in discussions with Chelsea about a contract extension despite having claimed last week that the player would definitely leave in the summer, when his deal ends. "Frank is under contract and he is doing fine," Benítez replied. "I know they have had conversations but the main thing for me is to bring the best out of him."

By the time Lampard had scored, it was hard to remember that Chelsea had at one stage looked in danger of losing this tie. The visitors had begun sluggishly against well-organised opponents and it did not come as a huge shock when Rodriguez, a surprise selection in attack over Southampton's top scorer Rickie Lambert, put his team ahead on 22 minutes with a low strike, having collected Jason Puncheon's through pass and run clean through following poor defending from César Azpilicueta and Gary Cahill.

It took going behind for Chelsea to wake up and, as has often been the case this season, Juan Mata proved to be their spark. Following a quick exchange of passes between Victor Moses and Eden Hazard, the Spaniard lifted the ball over Boruc and presented Ba with the opportunity to open his Chelsea account on 35 minutes, with the Senegal striker getting in front of Steven Davis to stab the ball into an empty net.

Ten minutes later, and after more relentless pressure from the visitors, it was 2-1, with Moses driving the ball in from inside the area. Branislav Ivanovic headed in Mata's cross to make it 3-1 before Ba got his second of the game, slotting in Hazard's cross from close range having done well initially to keep possession for Chelsea while under pressure from José Fonte. The Southampton captain injured his knee in the tussle and had to be carried off on a stretcher soon afterwards.

Lampard added to the Saints misery late on following Davis's handball. The holders march on.