Gauff, the reigning US Open champion and a former Roland Garros runner-up, rallied to win 4-6, 6-2, 6-3 on Court Philippe Chatrier and will face either tournament favourite Iga Swiatek or Marketa Vondrousova for a place in the final.
"She's a tough opponent and she's well loved on tour and I could tell by the crowd you guys wanted her to win. When I'm not playing, I do too," Gauff told the crowd, who had largely been cheering on Jabeur.
"I like playing in atmospheres like this. I know you wanted her to win but even when I was in the bathroom, I was thinking this is really fun, win or lose."
It will be American star Gauff's third successive Grand Slam semi-final, after also making the last four at this year's Australian Open.
Tunisian eighth seed Jabeur is still waiting for a maiden major title, having lost three finals and four quarter-finals.
Jabeur edged a tight first set on her third set point thanks to a break in the seventh game of the match.
But Gauff roared back, breaking Jabeur's serve three times in the second set to force a decider.
The 20-year-old grabbed a crucial break in game four and closed out victory on her third match point, as Jabeur fired a simple smash wide, to set up a possible repeat of the 2022 final with Swiatek.
"Today I was trying to be aggressive towards the end and I got a little bit tight on the couple of match points but I think I did what I needed to do to win the match," she added.
Gauff has lost 10 of her previous 11 meetings with Swiatek, all in straight sets, including in each of the two previous French Opens.