Vinci next plays Magdalena Rybarikova of Slovakia, who only needed 50 minutes to cruise past wild card entrant Ipek Soylu of Turkey 6-0, 6-0.
There were five breaks of serve in a back-and-forth second set, but again Errani made the crucial break in game nine and took the victory on her second match point. Stosur now has a 5-2 win-loss record against Koukalova.
Sevastova, who came out of retirement this season, had beaten Stosur in their only previous match – at the China Open in 2010, when Stosur was ranked seventh. Stosur, who won the Strasbourg title on red clay in May, will play Danka Kovinic for a semifinal spot. “I feel very comfortable, now I want to win the next match”.
Fifth seed Lucie Hradecka did not fare as well, though, as she exited 6-3 6-2 to Polona Hercog.
Russian qualifier Daria Kasatkina rallied to beat former champion Julia Goerges 3-6, 6-4, 6-3 and reach her first career quarterfinal at the Gastein Ladies on Thursday.
The Brazilian meets 18-year-old Alexander Zverev of Germany, who ousted fourth-seeded Juan Monaco of Argentina 6-4, 6-2, in an 80-minute game to reach his second World Tour quarterfinal.
The final second-round match between the third-seeded Karin Knapp of Italy and Johanna Larsson of Sweden was suspended because of a thunder storm and rescheduled for Friday. The match had been interrupted because of rain on Monday at 5-5 in the second set.