Olaru, who lost to Germany's Andrea Petkovic in last year's final, served 11 double faults but converted her seventh match point. Woerle has yet to win a singles match on the WTA Tour this season.
Alize Cornet of France routed Arantxa Rus of the Netherlands 6-2, 6-0 to set up a second-round match against either the top-seeded Petkovic or Iveta Benesova.
Story continues below ↓advertisement | your ad hereEarlier Monday, Mariya Koryttseva of Ukraine saved a match point before beating Tatjana Malek of Germany 6-7 (2), 7-6 (3), 6-2.
The 132nd-ranked Koryttseva rallied from 4-0 down in the second set and saved the match point when Malek was serving at 5-4.
Simona Halep of Romania also advanced by defeating Renata Voracova of Czech Republic 7-5, 6-2.
The $220,000 Gastein Ladies is the final clay-court tournament of the WTA Tour season.
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