Stosur was the first of the pair to advance to the semifinals, breaking serve three times and never facing a single break point herself to fend off WTA Rising Star Danka Kovinic in 66 minutes, 6-3, 6-2.
"I feel like today was definitely the best I've hit the ball and played all week," Stosur said.
"It's a good thing going into the semifinals. The conditions can help my second serve - the altitude makes the ball bounce very high, and I think my opponents are finding it difficult to control that. So if I can keep starting points like that, on my terms, that's definitely the way I want to be playing.
"To go through a match not facing a break point, it definitely shows I'm serving well."
Schmiedlova has now won eight matches in a row - five to win Bucharest last week and three here.
"I'm feeling great. I really like it here," the Slovak said. "It's been a good few weeks for me and I was really happy with the way I played today as well. I'm looking forward to the semifinals now."
Stosur beat Schmiedlova in the pair's only meeting, though it was totally different circumstances.
"I played Anna one time at Wimbledon a couple years ago, when she was pretty new to the tour, and she was much less experienced than she is now," Stosur said. "She's much more experienced now and has been having some great results, so obviously I won't be walking myself into the final!"
The Australian was asked about the potential dream final against Errani.
"I'd love for that to happen," she commented. "I'll certainly try my best tomorrow."
The No.1-seeded Errani followed Stosur into the semifinals a little later in the day with a hard-fought 6-3, 3-6, 6-2 win over Russian qualifier Daria Kasatkina. Errani was originally up a set and a break, leading 6-3, 3-2, but ended up having to go to three to fight off the WTA quarterfinal debutante.
Knapp leads Errani in their head-to-head, 3-1, though Errani's win came in their last meeting.
? WTA Gastein (@WTAGastein) July 24, 2015