Cheered on by compatriot and four-time grand slam champion Kim Clijsters from the stands, Wickmayer dominated play from the baseline to leave the 17th seed chasing shadows on a warm and sunny day at southwest London.
The result condemned Stosur to her sixth first-round exit at the grasscourt major, a tournament where she has failed to progress beyond the third round in 12 visits.
"(I'm) pretty annoyed about it, to be honest. I don't have an answer because I do feel I played well," the 30-year-old Australian said.
"That's that. I still think I'm a good enough player to get through first rounds here, and for whatever reasons it's not happening. It sucks."
Wickmayer will next face Croatia's Ana Konjuh for a place in the third round.
(Reporting by Pritha Sarkar, editing by David Goodman)
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