Ba quickly went about making an impact at his new club, drawing Chelsea level with a goal that proved the catalyst to a 5-1 win.
The Senegal international had not been sure if the first one was his after hitting home a Juan Mata effort on the line, although his second was far more clear-cut.
Ba slotted home impressively under pressure but was not going to try and wrestle Chelsea's late penalty off Frank Lampard in the search of a hat-trick.
"I'm not that crazy," Ba said, after Lampard fired home to put him joint second in Chelsea's all-time scorers list with Kerry Dixon.
"I don't think I have made a debut like that before. That's a great one and I'm pleased, I'm going to enjoy it a little bit.
"It's great, when you see the fans they show you they're happy for you, and the team-mates, when they come and congratulate you it's a good feeling.
"The three behind me make football look easy. I just try to run in behind and try to create space as well for them.
"I know when they have some space they will be very dangerous."
The brace at Southampton was the ideal end to what has been a whirlwind week for Ba.
"I woke up on Wednesday and I prepared myself to play (for Newcastle) against Everton," he said.
"I got a text from the manager that said I needed to come and see him.
"From that moment I knew that everything was fixed and I'd go.
"I travelled down as quickly as possible to London to watch the (Chelsea) game against QPR, and the next day I had a medical, so it was very busy.
"Now I'm just going to have one day off chilling with my kids and just relax."