Francesca Schiavone beat Anastasia Pavlyuchenkova 7-6 4-6 6-2 to seal victory in the fourth rubber of the semi-final for 2006 winners Italy, who were at home on clay at Castellaneta Marina.
"It's unimaginable. What they've done is extraordinary," Italian captain Corrado Barazzutti said after seeing his side reach their third final in four years. "These girls will go down in the history of Italian tennis."
Svetlana Kuznetsova had blasted away Flavia Pennetta 6-0 6-3 earlier to give Russia, winners of four of the last five Fed Cups, hope after they lost both of Saturday's singles.
Pennetta had no answer to the power and precision of the world number nine, who tidied up her act after piling up errors in Saturday's defeat to Schiavone.
Pavlyuchenkova looked like she might continue the comeback after taking the place of Anna Chakvetadze, who was out of sorts in her defeat to Pennetta on Saturday.
The 17-year-old showed no initial nerves in her first Fed Cup rubber, breaking Schiavone in the opening game and then holding to love.
The 44th-ranked Italian is a fighter, however, and she won the next four games on the way to taking the first set in a long tie-break.
Pavlyuchenkova, ranked 28th, pulled back in the second but Schiavone held her nerve to weather some early pressure in the final set and ease home.
Roberta Vinci and Sara Errani wrapped up Italy's first Fed Cup victory over Russia with a 1-6 6-3 6-4 doubles win over Nadia Petrova and Pavlyuchenkova.
America's Fed Cup debutante Bethanie Mattek-Sands made amends after losing both her singles matches by combining with the world's top-ranked doubles player, Liezel Huber, to clinch the deciding match in Brno in dramatic fashion.
The duo saved a matchpoint in coming back from a set and 5-2 down to beat Iveta Benesova and Kveta Peschke 2-6 7-6 6-1.
Another newcomer, Alexa Glatch, ranked 114th, was the Americans' biggest heroine, thrashing fellow 19-year-old Petra Kvitova 6-2 6-1 to keep her team in the tie with her second victory when they were 2-1 down.
"This has been unbelievable," Glatch said. "I'm playing really good tennis and I'm just stepping up to the plate.
"I did a good job of not giving her (Kvitova) any short balls, really keeping it deep and not allowing her to step in and take charge of the point."
Lucie Safarova, brought into the singles after Glatch surprisingly whipped Benesova on Saturday, had put the Czechs in front in the day's first game with an easy 6-3 6-1 win over Mattek-Sands.
The USA, who had been expected to struggle as none of their top players had turned up for the tie, have made the final for the first time since 2003.
They will take on Italy in November with the aim of securing their 18th title, after their last win in 2000.