Ormaechea made a bright start, attacking the Errani serve and breaking twice to build a 3-1 lead. However, Errani hit back in spectacular fashion, reeling off the next 11 games to complete a 6-3, 6-0 win.
In seven previous visits to Bad Gastein, Meusburger had never lost before the quarterfinals, and when she took a tight opening set it looked like this record would stay intact.
Scheepers had other ideas, racing through the second set before overcoming a couple of early breaks and a rain delay to take an equally one-sided decider.
The other quarterfinal in the bottom half will see No.7 seed Camila Giorgi take on qualifier Shelby Rogers. Giorgi enjoyed a productive grass court season and has transferred this form to the clay, easing past wildcard Lisa-Maria Moser, 6-0, 6-2, in little over an hour.
World No.147 Rogers caused the biggest shock of the week by knocking out No.3 seed Carla Suárez Navarro, 6-4, 6-0. The turning point for Rogers, who had never previously been beyond the second round of a WTA event, came when she prevailed in a marathon final game of the opening set. From here, the Spaniard's resistance wilted, Rogers racing through the second set in just half an hour to record her first win over a Top 50 player.