Errani, ranked seventh in the world, dispatched Irina Khormacheva 6-1, 6-4 in the second rubber following a grueling three-set victory by Vinci over unheralded Alexandra Panova.
The Italian squad can clinch the Fed Cup Sunday in reverse singles and a doubles rubber. It would be the first Italian championship since 2006.
Russia, which fielded an undermanned team -- with no players ranked higher than 135th -- will try to rally for its first Fed Cup since 2007. The Russians were without injured Maria Sharapova and a bevy of other international stars who were unavailable to compete.
The Russians performed gamely in the first match Saturday, with Panova keeping Vinci on the court for more than 3 hours before succumbing 5-7, 7-5, 8-6. Panova led 3-2 in the third set but Vinci saved four match points in the home stretch to secure the victory.
Vinci will face Khormacheva Sunday.