Safina, the highest ranked woman ever to compete in the Portoroz tournament, made her 277th ranked opponent nervous at first as she swept to take the first set, conceding only eight points.
Safina was broke by the 18-year-old Slovenian in the third game in the second set but soon recovered to break in the ninth.
Also Monday, third-seeded Kaia Kanepi of Estonia was upset by Olga Gotortsova of Belarus, 6-1, 6-2.
Sixth-seeded Lucie Safarova of the Czech Republic advanced by beating Katie O'Brien of Britain 6-4, 6-4 while Petra Martic of Croatia ousted Kristina Barrois of Germany 6-3, 6-4.
Klara Zakopalova of the Czech Republic, the 2005 champion, beat Slovenia's Masa Zec Peskiric 6-2, 6-4, and Rossana De Los Rios of Paraguay defeated Viktoriya Kutuzova of Ukraine, 5-7, 6-4, 7-6 (6).
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