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Bartoli was aiming to cap her recall to the Fed Cup team this week after a nine-year exile with a maiden triumph in the French capital, but the world number 10 came up short as she faltered badly at key moments.
The third seed, runner-up in last year's tournament, led 6-2 in the first-set tie-break but squandered four set points as Barthel, ranked 45th, escaped from a perilous position to move in front.
The German then secured an early break that proved decisive in the second set with Bartoli unable to offer any resistence to Barthel's serve.
Barthel will now face either Czech Petra Kvitova or French teenager Kristina Mladenovic in the semi-finals.
Italian top seed Sara Errani avenged her defeat to Carla Suarez Navarro at last month's Australian Open, as she edged past the Spaniard to reach the last four.
World number seven Errani was a first-round casuality in Melbourne following a straight sets loss to Suarez Navarro, but the Italian demonstrated her typical craft and determination to earn a gruelling 7-5, 4-6, 7-5 win in just over three hours.
Both players struggled to hold serve in the first set in the French capital, but it was Errani who made the decisive breakthrough at 5-5 before proceeding to serve it out to take the lead.
Navarro refused to cede any ground in the second set though and she eventually prevailed as Errani crumbled on serve, sending the contest into a decider.
The Spaniard then had a chance to claim the scalp of the tournament's top seed at 5-4 in the third, but a battling Errani fended off a match point and went on to level the score at 5-5.
Suarez Navarro was then left to rue her missed opportunity as Errani broke before closing it out on serve to seal victory and set up a meeting with Kiki Bertens of the Netherlands.
Earlier, Bertens followed up her second-round win over Dominika Cibulkova -- her first triumph over a top 20 opponent -- by casting aside 18th-ranked Lucie Safarova 6-1, 7-5 to reach her first semi-final at a premier event.
The 21-year-old, who made the main draw as a lucky loser following the illness-enforced withdrawal of Czech Lucie Hradecka, broke sixth seed Safarova three times as she cruised through the opening set.
Bertens then again broke her Czech opponent early in the second set to seize the initiative before Safarova recovered to level at 4-4.
But a loose service game at 5-5 from Safarova presented Bertens with the opportunity to serve for a place in the semis and she took full advantage, closing it out with an ace on her first match point.
"It's been an amazing week. My tennis is going very well, I'm very happy with that," said a smiling Bertens.
"I think I played well today. I was concentrated from the first point and I think that was a good thing.
"I'm playing very good and I hope that can continue tomorrow," added the world number 65, who will face Errani for a place in Sunday's final.