The world number five lost to a player ranked almost 200 places below her after serving up seven double faults, with Belgian Flipkens powering nine aces past the Australian.
Stosur, who lost to the similarly lowly Melanie Czink in the first round at Wimbledon last year, is left short of grass-court practice ahead of her trip to the All England Club
The 2011 US Open champion started well, breaking twice to move 4-0 ahead in the first set.
But an unforced error on break point saw Stosur mis-hit a smash to lose her advantage, doing likewise on a forehand volley at 5-5.
She then threw away three set points on the tie-break, losing that 9-7, before collapsing in the second set and handing Flipkens an early break with a poor double fault, the Belgian holding her nerve and serve to clinch a famous victory.
Second seed and French Open finalist Sara Errani also suffered defeat, the Italian losing 5-7 6-3 6-4 to Kateryna Bondarenko of Ukraine, while fifth seed Maria Kirilenko also tumbled out, although the Russian’s 6-4 3-6 7-5 loss to experienced Italian Francesca Schiavone was less of an upset.
Some of the top seeds did go through, as third-seeded Slovakian Dominika Cibulkova beat Romania’s Alexandra Cadantu 6-2 6-2, while sixth seed Roberta Vinci of Italy and eighth seed Nadia Petrova of Russia progressed with victories over Greece’s Eleni Daniilidou and local player Kiki Bertens.
In the men’s action third seed Juergen Melzer of Austria beat Russia’s Igor Kunitsyn 6-1 6-1, while fourth seed Robin Haase went out in his homeland with a 6-4 7-6(2) loss to Mate Pavic of Croatia.