The pair were among three seeds in action but suffered surprise defeats to Tereza Smitkova and Richel Hogenkamp respectively in the WTA 125K series hard-court event.
Van Uytvanck of Belgium threw away a one-set lead against her Czech opponent to bow out 3-6 6-2 6-2 as Smitkova bolstered her head-to-head record to 2-1 in career meetings with the sixth seed.
Dutch world number 148 Hogenkamp saw her dream start to the competition continue, as she accounted for seventh seed Voegele of Switzerland in straight sets.
Hogenkamp gained entry to the competition as a lucky loser following the withdrawal of top seed Alize Cornet due to a back injury.
And the Dutch competitor continued to take full advantage of her late entry as she moved into the third round, after seeing off Lourdes Dominguez Lino of Spain in her opener.
Having saved five of six break points in the match, Hogenkamp potentially faces a third-round clash with fifth seed Anna Schmiedlova who is due to take on Andreea Mitu.
While Van Uytvanck and Voegele saw their campaigns ended, there were no such struggles in the end for second seed Caroline Garcia after the French world number 38 recovered from a set down to edge Timea Babos.
Garcia came through a marathon encounter to see off the Hungarian 6-7 (4-7) 6-1 6-3 in their opening match and will now face Kazakhstan's Yulia Putintseva.
There was further joy for the home crowd later in the day's play as French wildcard Oceane Dodin proved too strong for Katarzyna Piter of Poland in a 6-4 6-0 triumph.
Elsewhere, Ana Konjuh and Francesca Schiavone also enjoyed straight-set wins as they knocked out Carina Witthoeft and Alexandre Dulgheru respectively.