German Goerges, who beat Australian Stosur in the last four en route to the Stuttgart title in 2011, was made to battle a lot harder by Russian Anastasia Pavlyuchenkova before edging past the world number 23 5-7 6-3 6-4.
"It is normal if I come here as defending champion," Goerges said. "Of course there will be expectations and the pressure is on you. I need to improve my game."
Fellow German Andrea Petkovic crowned her comeback on the tour after more than three months out with a back injury with a confidence-boosting 6-1 6-4 victory against wild card Kristina Barrois to set up a second round clash with world number one Victoria Azarenka.
World number seven Marion Bartoli also moved into the second round with a trouble-free win over Czech Iveta Benesova.
Former Wimbledon finalist Bartoli pinned the Czech back with a barrage of groundstrokes and got the first break to lead 3-2 in the first before breaking again to clinch the set with a powerful two-handed backhand down the line.
Qualifier Benesova broke straight back in the first game of the second set but Bartoli upped her game again to ease home.
World number eight Li Na needed a tie break to grab the first set against Czech Lucie Safarova but got a quick early break to clinch a 7-6 6-4 victory.
At the concurrent WTA tournament in Fes, second seed Svetlana Kuznetsova came through her first round match with a 6-1 7-5 win over Greece's Eleni Daniilidou.