Flavia Pennetta's withdrawal due to an ankle injury meant Ukraine's world number 35 went into her second-round clash with Voegele as the fourth-highest seed left in the competition.
However, her hopes of progressing to the last eight of the WTA International clay event were ended by the 24-year-old Swiss 6-2 7-5.
Voegele hit six aces and saved four of six break points in the match to win the pair's first meeting and set up a quarter-final meeting with Andrea Petkovic.
Fourth seed Petkovic remains on track for a second title in Bad Gastein after edging Dinah Pfizenmaier.
German Petkovic, 2009's champion, began well in Wednesday's 6-1 6-3 success over compatriot Pfizenmaier - reeling off five consecutive games to take the first set.
Petkovic won 10 of 13 first service points in the second set and the world number 20 dominated her opponent's second serve in a strong showing.
Eighth seed Karolina Pliskova avoided adding her name to the list to beaten seeds as she dispatched Romanian qualifier Ana Bogdan in straight sets.
Perhaps unsurprisingly given the pair's 260-place separation in the rankings - the Czech world number 48 broke Bogdan in all four of her service games in the first set and twice more in the second to progress.
Pliskova has just one WTA title to her name - the 2013 Malaysian Open - but will be one step away from the final if she overcomes America's Grace Min in the quarter-finals.
The 20-year-old was too strong for compatriot Irina Falconi - winning through 6-3 6-3 after the Ecuador-born qualifier double-faulted five times in the match and won only 57 per cent of points on her first service.