The 27-year-old completed his move from Newcastle to west London on Friday and made his Blues debut a day later in their FA Cup third-round tie at Southampton.
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, with Lampard firing 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 after that 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."
The move ended Ba's short but successful 18-month stay at St James' Park in which he scored 29 goals in 54 league appearances.
"When a club like Chelsea wants you the decision is going to be easy," he said.
"With all the respect I have for Newcastle, because Newcastle is a big club with a big history, when you come to Chelsea it's a step forward for me.
"They (Newcastle supporters) probably won't be too happy but the true fans will understand.
"They were supporting me from day one and I'm very happy with this season. They're some of the best fans I've played for.
"I just want to thank them for what they've done for me.
"I can understand. It's not like I wanted to leave them in some trouble but if you have Chelsea wanting you this kind of club is not coming in every day for you."
Ba's arrival and immediate impact has raised questions as to whether he can play alongside the rejuvenated Fernando Torres.
"Ask the manager," he said. "If I have to play with him, I'll play.
"If I have to be on the bench, I'll be on the bench and wait for the chance and if he puts me on the pitch I'll prove I can play. That's it."