Trailing 2-1 in the quarterfinal round entering Sunday's action, Italy kept its hopes alive when Vinci posted a 6-2, 4-6, 6-1 decision over Jamie Hampton to force a fifth and deciding doubles rubber.
Then, with the match on the line, the Italians dropped their scheduled doubles duo of Nastassja Burnett and Karin Knapp and replaced them with Vinci and Errani -- a tandem that won last month's Australian Open title.
The move paid dividends when they breezed past the American team of Varvara Lepchenko and Liezel Huber 6-2, 6-2 to clinch the weekend series.
The victory moved Italy into April's Fed Cup semifinals against the defending champion Czech Republic, which moved on with a with a 4-0 triumph over Australia earlier Sunday.
2014: The Year in Music [PHOTOS]