Germany's Georges, the world number 24, was ousted in one hour and 42 minutes by the unseeded Slovene, who beat Sweden's Johanna Larsson in last year's final.
Fifth seed Anastasia Pavlyuchenkova and seventh seed Mona Barthel both made it safely into the third round though.
Germany's Barthel saved 11 break points in a great battle against Kateryna Bondarenko of Ukraine 6-2 7-5, with Barthel's superior serving ultimately the telling difference between the two players.
Russia's Pavlyuchenkova, meanwhile, came through a close opening set before going up a gear to beat Spain's Silvia Soler Espinosa 6-4 6-0.
Bulgaria's Tsvetana Pironkova also won, beating Ukraine's Lesia Tsurenko 7-5 6-3.
In the remaining first-round matches local hope Johanna Larsson made it through when Olga Govortsova of Belarus retired while trailing 7-6(6) 4-3.
Top seed Sara Errani withdrew on Tuesday, citing a shoulder injury.