Former world No. 1 Wozniacki, seeking her first victory in a year, overcame home crowd favorite Mandy Minella of Luxembourg 6-3, 7-6 (7-2) to gain the second round.
Second-seeded Stephens, meanwhile, continued her surprising season with a 6-3, 6-3 spanking of Swiss wild card Timea Bacsinszky. She reached the semifinals of the Australian Open in January and followed that up with strong showings at Wimbledon and both the French and U.S. Opens.
Her next opponent Austrian Yvonne Meusburger, who posted a a 6-4, 6-2 triumph over Romania's Irina-Camelia Begu.
Also moving on was No. 3 seed Sabine Lisicki, who rallied to defeat Croatia's Donna Vekic, 2-6, 6-3, 6-0.
The news wasn't as good for fourth-seeded Kirsten Flipkens of Belgium, however. She fell victim to Polish qualifier Katarzyna Piter 6-4, 6-2 in an opening-round match.
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