The 27 year-old is the new title favourite, after Iga Swiatek's third-round exit, as she chases a maiden grand slam title.
Jabeur was made to work hard for a 7-6 (11-9) 6-4 victory over Belgian Elise Mertens, but she has still yet to drop a set.
Next for Jabeur is Czech player Marie Bouzkova, the world number 66, and she is relishing her role as a trailblazer for African and Arab women.
"I enjoy sometimes failing and succeeding after. It's amazing," Jabeur said. "I wish I could really give the message to the young generation, not just from my country but from the African continent.
"I want to see more players here, I want them to believe more in themselves and believe that they can be here. I don't come from a rich family, so you have to really stop finding excuses and go for it, just be yourself and enjoy playing tennis."
World number two Jabeur is the only Tunisian ranked inside the WTA top 700. This is her fifth Wimbledon, and last year's run to the last eight was her best performance at that point, with Aryna Sabalenka preventing her going any further.
Now she has the title in her sights.
"It's amazing to be here and hopefully I can continue," she said in an on-court interview. "I love playing on grass. I love the connection between nature and me, so hopefully it will continue this way for me and maybe through to the finals."
Mertens beat former champion Angelique Kerber in round three, and against Jabeur on Court One she battled from an early 3-1 deficit to force the opening-set tie-break.
It was exhilarating at that point, and Jabeur was relieved to win the breaker, fearing she might not have the wherewithal to come back from dropping the set.
Mertens beat Jabeur in round three at the US Open last year, so the threat she posed was clear.
"She's a great opponent really. It's never easy to play her, and I had to dig deep, very deep, in the tie-break," Jabeur said. "I couldn't imagine myself playing three sets against her."