Errani knocked off Lucie Safarova 6-2, 6-4 and Vinci followed with a 6-4, 6-1 victory over Petra Kvitova.
The winner of the series will advance to the finals in November against either Russia or the Slovak Republic.
The Slovak Republic notched two singles victories Saturday in the opening matches to take a 2-0 lead in their Fed Cup semifinals series against Russia.
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