Vinci piled up seven service breaks over the final two sets of a 1-6, 6-1, 6-1 win over Mathilde Johansson. Vinci won only about one-third of the points in the first set but charged back and took nearly 70 percent in the last two sets.
That includes 74 percent receiving serve -- the only two games she lost after the first set were on her own serve.
No. 6-seeded Petra Cetkovska was also pushed to three sets before she advanced with a 6-1, 5-7, 7-5 victory over Shahar Peer. Cetkovska finished off all four of her break-point chances in the third set.
Sara Errani, the seventh-seed, topped Irina-Camelia Begu 7-6 (7-5), 6-4 by converting a pair of second-set break opportunities.
Simona Halep defeated Sloane Stephens 6-4, 6-4 and Garbine Muguruza Blanco got past Arantxa Parra Santonja 6-3, 6-3.