Stephens, the No. 2 seed, took just less than 60 percent of the points overall for a 6-3, 6-1 rout of Magdalena Rybarikova. Two of the games Stephens lost were on breaks but she had six breaks herself and won 29-of-48 of the points off Rybarikova's serve.
Seeded players went 5-1 in Tuesday's play. The exception was Patricia Mayr-Achleitner's 1-6, 6-3, 6-4 win over sixth-seeded Sorana Cirstead. After the shaky first set, Mayr-Achleitner saw just two break points while posting a pair of breaks in each the second and third sets.
Third-seeded Ana Ivanovic also sailed through the first round, taking out Yanina Wickmayer 6-2, 6-4 with five breaks in Wickmayer's nine games servicing. No. 4-seeded Carla Suarez Navarro claimed a 6-2, 6-3 win over Kristyna Pliskova and fifth-seeded Kirsten Flipkens came from behind for a 2-6, 6-2, 6-2 win over Donna Vekic.
The other seeded winner Tuesday -- seventh-seeded Dominika Cibulkova -- took 71 percent of the points over the second and third sets for a 3-6, 6-2, 6-1 decision over Annika Beck.
Also Tuesday, Andrea Petkovic defeated Yvonne Meusburger 6-3, 7-5; Katarzyna Piter got by Irina-Camelia Begu 6-2, 4-6, 6-3; Camila Giorgi beat Julia Goerges 6-2, 6-3; and Maryna Zanevska took out Aleksandra Krunic 7-5, 2-6, 6-2.
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