Vinci defeated Lucie Safarova 6-3, 6-7 (2-7), 6-3 in a 2 1/2-hour match, giving the Italians a 3-1 lead in the best-of-five semifinal. The doubles match wasn't played.
Italy will be going for its fourth Fed Cup title in November when it plays Russia. Italy won three of five titles from 2006-10. Russia won four of five Fed Cups over the 2004-08 period. Russia defeated Italy for the 2007 championship.
The Czechs lost both of Saturday's singles matches in straight sets. Petra Kvitova kept the Czechs' alive in the series with a three-set win Sunday but rain and darkness forced a suspension of play, leaving Vinci and Safarova to meet early Monday.
Vinci, who rolled over Kvitova Saturday with eight service breaks, cashed in her only break chance of the first set Monday to grab the lead. Both players had three breaks in the seesaw second set, which Safarova won in the tiebreaker.
Safarova jumped ahead 2-0 in the third set but Vinci immediately broke back. The set remained tight until the eighth game when Vinci posted her sixth break of the day. Safarova fought off two match points but Vinci won her third chance to close the match.
Russia rallied from 0-2 down in defeating the Slovak Republic 3-2 with three wins Sunday.
The 2013 Fed Cup final is set for Nov. 2-3.
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
LGBT community has 'bullied the American people': Bachmann