"It definitely helped to bring a lot of inner confidence in myself, knowing that I can do it, " said the 23-year-old, who will play 54th-ranked Romanian Monica Niculescu.
The Dane, seeking a first grand slam title and needing to reach the last eight to have a chance of staying top of the rankings, beat Romanian 31st seed Monica Niculescu 6-2 6-2.
Fifth seed Stosur , who was runner-up to Schiavone at Roland Garros, came from behind to beat Elena Vesnina 3-6 7-6 (7-2) 6-1, and number 10 seed Azarenka overcame a blip to beat Monica Niculescu 6-0 5-7 6-1.