The 29-year-old Scot, who required foot surgery in October, battled through in 119 minutes against the 58th ranked Swiss.
Baltacha has slipped to 234 in the world rankings after nearly 10 months out of the game but will now face Jana Cepelova for a place in the quarter-finals.
Caroline Wozniacki is top seed for French Open warm-up at the Primrose Royal Tennis Club in the north of the Belgian capital.
Brussels: Round 1 results
Elena Baltacha (GBR) beat Stefanie Voegele (Switzerland) 7-6 7-5
7-Varvara Lepchenko (USA) beat Bojana Jovanovski (Serbia) 6-2 6-7(8) 6-4
Jana Cepelova (Slovakia) beat Lesia Tsurenko (Ukraine) 5-7 6-3 7-5
Olga Govortsova (Belarus) beat Arantxa Rus (Netherlands) 6-2 7-5
- Sports & Recreation
- Jana Cepelova
- Caroline Wozniacki