The 54th-ranked Kanepi was the highest ranked player left in the tournament after early defeats for the top eight seeded players. Barthel won on the first of two match points.
Barthel, chasing her third WTA title, next plays Silvia Soler-Espinosa. The Spaniard - a first-time finalist in Strasbourg in May - beat Russia's Alexandra Panova 6-3, 6-2.
In the other quarterfinals, Chanelle Scheepers of South Africa defeated Spain's Lara Arruabarrena 6-2, 4-6, 6-3, while Slovakia's Jana Cepelova beat Yulia Putintseva of Kazakhstan 6-4, 7-5.