Schiavone dropped the first set in the match in Ukraine but cruised in the next two, winning 2-6, 6-1, 6-1.
The win put the Italians ahead 3-1 in the best-of-five matches and moved them into the semis against the Czech Republic, which scored a quarterfinal win over the German team.
Earlier, Flavia Pennetta had given Italy a 2-1 lead with a 7-5, 7-6 (7-3) decision over Alona Bondarenko, Kateryna's younger sister.
Italy beat the United States in last year's Fed Cup final.
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