A 6-2 6-3 win over Diane Parry in 68 minutes was the longest amount of time Jabeur has spent on court at the All England Club this summer, and means she has only played a little more than three hours in SW19 so far.
The third seed was in superb touch against her French opponent and showed her full repertoire of tricks on Centre Court with several trademark drop shots able to help her into the last-16.
In the men’s competition, Novak Djokovic comfortably reached the last 16 at Wimbledon on Friday while Maria Sakkari became the sixth top-10 women's seed to crash out in the first week.
Three-time defending champion Djokovic demolished Serbian compatriot Miomir Kecmanovic 6-0, 6-3, 6-4 to stay on course to pull level with Pete Sampras as a seven-time champion, one behind Roger Federer's men's record.
“So far, so good,” said the 35-year-old top seed after beating a player who described him as his “idol”.
“I expect high standards from myself. You always want to raise the level and things are shaping up well.”
Waiting in the fourth round is Dutch wild card Tim van Rijthoven.
Back in the women’s draw, Elise Mertens, who downed former Wimbledon champion Angelique Kerber 6-4 7-5, stands between Jabeur and a place in the quarter-finals.
Jabeur, one of the favourites for the title, said: “Hopefully I will be even better for the next matches.
“I am playing the tennis that I love to see. Obviously there's a few things to improve and I want to be challenged for the next round, for sure, and see how I handle that pressure.
“For me, sometimes I start playing not so good. I feel like at the end of the tournament I start playing better and better. When I get more matches and I get used to the courts, to the environment here, I think I start to play better.”
After racing through her opening two matches with Mirjam Bjorklund and Katarzyna Kawa, a similar pattern developed in this third-round tie after Jabeur broke three times in the first set.
Tatjana Maria provided the big shock on day five by knocking out Maria Sakkari.
Fifth seed Sakkari had beaten the German at the Australian Open in January but suffered a 6-3 7-5 loss in one hour and 30 minutes on Court Two.
It secured world No 103 Maria a maiden appearance in the fourth round of a grand slam.
“I'm the first time in the last 16, so that's already amazing, and to win against Sakkari today, yeah, it's pretty awesome,” she added.
Maria will next take on Jelena Ostapenko, who beat the German and her partner Oceane Dodin in the women's doubles on Thursday.
Twelfth seed Ostapenko was the first woman into the fourth round but needed three sets to get the better of Irina Begu 3-6 6-1 6-1.
Jule Niemeier also progressed and in the process ended the run of Ukraine's Lesia Tsurenko.