Second-seeded Wickmayer sped past American Alison Riske 6-3, 6-3 in one of the first-day matches, converting 5-of-6 break opportunities in the victory.
Meanwhile, No. 2 seed Barthel struggled against Britain's Heather Watson, but eventually claimed a 6-7 (5-7), 7-6 (7-5), 6-1 victory in 2-hour, 38-minute battle.
The news wasn't as good for fifth-seeded Swiss Romina Oprandi, however. She was upended 6-1, 7-6 (13-11) by German Annika Beck.
Germany's Tatjana Malek also took a first-round match Monday, besting American Alexa Glatch 7-6 (7-3), 6-3.