Early exits for all eight seeds had left World No.54 Kanepi as the highest-ranked player in the draw, but she was no match for an on-song Barthel, who weathered a late storm to triumph, 6-2, 7-6(4).
After an early exchange of breaks, Barthel reeled off four straight games to run away with the opening set. The second set was a far closer affair, going with serve until the ninth game when Kanepi found the line with a forehand return to break.
Eager not to be outdone in the shotmaking department, Barthel hit straight back with a precise backhand pass. In the subsequent tie-break, it was the backhand that once again proved the difference, a crosscourt pass taking the German to two match points. She only needed the one, another crisp backhand booking a last four meeting with Sílvia Soler-Espinosa.
"That was a really tough match, especially in the second set," Barthel said. "It was really close and she served for the set.
"I'm pretty happy I stayed tough in these moments, believed in myself and just kept going for my shots. I played a really good tie-break in the end and I think this made the difference."
Soler-Espinosa was equally impressive against Alexandra Panova, needing little over an hour to complete a 6-3, 6-2 win.
"Of course it was a tough match, because everyone who is in the quarterfinals is playing well," Soler-Espinosa said. "I knew she was going to be quite solid from the baseline, so I just tried to play my game, be aggressive and use my forehand to move her when I had the opportunities. I'm so happy to be in the semifinals here in Bastad!"
Having saved two match points during her second round win over qualifier Laura Sigemund, Scheepers was once again pushed the distance, defeating Lara Arruabarrena, 6-2, 4-6, 6-3. In the final match on Center, Cepelova recovered from a slow start to overcome Yulia Putintseva, 6-4, 7-5.