Jabeur climbed to No.2 in the world on Monday, then celebrated with a commanding 6-1 6-3 victory over Swedish qualifier Mirjam Bjorklund to be the first big gun through to the second round of Wimbledon 2022.
The straight-sets win atoned for a shock first-round French Open loss to Magda Linette in her most recent grand slam outing.
"I don't like to make the mistake twice," Jabeur said.
"I learned a lot from the first round in Roland Garros. Obviously, everything feels different here. I feel, like, more ready."
A quarter-finalist last year, Jabeur arrived at the All England Club a fortnight after claiming her maiden grass-court title in Berlin and fresh off being hand-picked by Williams to be the 23-times grand slam champion's partner in her much-anticipated return to tennis from a year-long lay-off.
"She's the queen on the court. That's a huge honour, great pressure for me to feel it," Jabeur said of her Eastbourne experience with Williams.
"I feel like maybe two or three years ago, if she did the same thing, I would have played horribly and not able to handle that kind of pressure.
"But now I feel like it was the right time that I play with someone like Serena.
"I gained more confidence playing along Serena. It also helped me with the great attitude on the court. Kind of start to be a leader on the court.
"That's what I'm trying to do. Trying to have that attitude."
The 27-year-old is the first African to reach No.2 in the rankings and hopes to inspire more to Arabs to play the sport as well.
More immediately, Jabeur has designs on Iga Swiatek's top ranking.
"Before in the beginning of the season," she said. "I don't feel I deserve the spot to be maybe five or four. Now I feel like I deserve it even more. I feel like I even gained and won matches to prove myself on this level.
"I do feel more confident. I do feel like I deserve to be in this level. Hopefully next step will be No. 1."
Third-seeded Jabeur will play either Polish qualifier Katarzyna Kawa or Canadian Rebecca Marino on Wednesday for a place in the third round.