Ba, who sealed a £7m move to Stamford Bridge from Newcastle on Friday, cancelled out Jay Rodriguez’s opener for the home side when he turned home Juan Mata’s shot in the 35th minute.
Victor Moses then gave the Blues the lead, before goals from Branislav Ivanovic, another from Ba, and a Frank Lampard penalty sealed an emphatic third-round victory at St Mary’s.
Benítez opted to rest Fernando Torres in favour of starting the Senegal striker – and the Chelsea interim boss was delighted with the forward’s instant impact.
“It is always important for a striker to score goals but more than just the goals was his contribution for the team,” said Benitez.
“His movement and understanding of things we were wanting to do was really good. He was very clever and he could understand the movement of the players. He did everything well on the pitch.
“I prefer to have this selection problem now than to have just one striker. It is important to have good players and different options, and Ba and Torres can compete or play together.”
The Chelsea boss added: “I will be delighted if we can carry on in all the cup competitions until the end because it means the team is doing well.
“Today I was trying to manage minutes with substitutions for Ivanovic and Mata, and I will try to do the same until the end of the season.
“We have a good record in the FA Cup and as a club and as a manager, but every game is different. We are happy because we progressed and have another chance to do well, but we will see what happens in the next round.”
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