Haddad Maia first Brazilian woman since 1968 in Grand Slam semi-final
World number 14 Haddad Maia came through 3-6, 7-6 (7/5), 6-1 and will face either top-ranked defending champion Iga Swiatek or Coco Gauff for a place in Saturday's championship match.
The 27-year-old left-hander follows in the footsteps of seven-time major winner Maria Bueno who was the last Brazilian woman in the semi-finals of a major at the US Open 55 years ago.
Bueno, who passed away in 2018, made the last four in Paris in 1966 before the advent of the Open era.
"Ons is not easy to play against, you have to be patient but I believed in my body and tried to keep my rhythm," said Haddad Maia.
Jabeur, the runner-up at Wimbledon and the US Open in 2022, was playing in her first quarter-final at Roland Garros.
The Tunisian hit 15 winners as she claimed an opening set which featured five breaks of serve in nine games.
Haddad Maia had never got past the second round of a Grand Slam before this French Open.
She had saved a match point in the third round against Ekaterina Alexandrova and then defeated Sara Sorribes Tormo in a three-hour 51-minute marathon, the third longest women's match ever played at the tournament.
She summoned all that fighting spirit in the second set against Jabeur, holding her nerve on a fourth set point.
Haddad Maia then swept into a 3-0 lead in the decider, saved four break points to stretch to a 5-1 advantage and took the match after two and a half hours when Jabeur hit long.
"I had a day off after my fourth round match. My amazing team worked hard on my body," said the Brazilian.
"We work hard all year to be in these moments so I remembered this when we were in the middle of the second set."