The Blues came into the match on the back of a shock defeat to west London rivals QPR and fell behind to a Jay Rodriguez effort after 22 minutes.Chelsea, though, rallied to turn the game on its head, running out 5-1 victors as Victor Moses, Branislav Ivanovic and Lampard efforts complemented a Ba brace.
The 27-year-old only completed his move from Newcastle yesterday and Chelsea interim manager Benitez was pleased with what he saw.
"The first half we had to work but after that little by little the team was getting better," he said.
"The second half was much better. We played with quality and when you're one goal ahead they have to take more risks.
Ba's display was so impressive that Fernando Torres, a player rejuvenated under Benitez, was left on the bench at St Mary's.
As well as Ba's debut goals, St Mary's also bore witness to some history courtesy of a late Lampard penalty.It saw the midfielder equal Kerry Dixon's all-time scoring record of 193 for Chelsea to put him joint second behind Bobby Tambling, whose record haul of 25 FA Cup goals Lampard levelled with in the process.
A bad afternoon was made worse for Saints when centre-back Jose Fonte was stretchered off in the second half.The Portuguese left St Mary's on crutches and in a leg brace with what Adkins confirmed was a knee injury.
"It is not good when somebody gets stretchered off," he said.
"He is being assessed now so I don't know the extent of the damage.
"It is a knee injury he has picked up but I don't know what yet."
Full coverage of all the FA Cup ties can be found here.