Errani, seeded fifth, disposed of Kirsten Flipkens of Belgium 7-6 (7-3), 6-1, while No. 10 Vinci advanced with a 6-2, 6-2 decision over Ukrainian Elina Svitolina.
Also posting Day 1 victories were 11th-seeded American Sloane Stephens, who dispatched Canada's Aleksandra Wozniak 6-4, 6-4, and No. 12 Carla Suarez Navarro of Spain, who got past Frenchwoman Kristina Mladenovic 6-2, 3-6, 7-5.
No. 16 Simona Halep of Romania fell in a minor upset to Urszula Radwanska of Poland 7-6 (7-4), 7-6 (7-2).
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