Lucie Hradecka and Kveta Peschke beat Maria Kirilenko and Elena Vesnina 6-4 6-2 to give the Czech's their first title as an independent nation after they split from Slovakia in 1993.
Wimbledon champion Petra Kvitova took the Czechs to within a point with a 4-6 6-2 6-3 win over Svetlana Kuznetsova.
Russia's Anastasia Pavlyuchenkova then beat Lucie Safarova 6-2 6-4 to level.Continue reading the main story
The Fed Cup is an international team event for women. Like the Davis Cup, ties are played in a best-of-five format with four singles and one doubles match. Nations are organised into groups, with the eight in the top-flight World Group playing a knockout competition to determine the champions
In Saturday's opening session, Kvitova gave the Czechs the lead by beating Kirilenko 6-2 6-2 before two-time Grand Slam winner Kuznetsova defeated Safarova 6-2 6-3 to get Russia back on terms going into the final day.
"Petra won two points, but we needed one more," said Czech captain Petr Pala. "I'm glad we've managed to (get) the third one. We all won it because victory is made of small pieces you have to put together. It's team work."
Russia captain Shamil Tarpischev also praised Kvitova, who won six times this season and climbed to number two in the world.
"The Czechs won thanks to Kvitova's superb play," Tarpischev said. "She was just great."
In the decider, the Russian pair broke early for a 4-2 lead, but the Czechs won four consecutive games to take the first set and then raced to a 5-2 lead in the second. The home duo saved three match points on Vesnina's serve before she sent a shot wide on the fourth.
"The Czechs played unbelievably well, they dominated the game and left us no chance," Vesnina said. "It was tough to get something going today, but we fought until the very end."
Kvitova and Kuznetsova traded breaks three times in the first set before the Czech, 5-4 down on her serve in the 10th game, netted a backhand to go 1-0 down in the match.
But Kvitova won five consecutive games in the second set and, trailing 3-0 in the decider, went on to close out the match with a backhand winner on her second match point.
"I wasn't playing my tennis in the first set, making too many mistakes, while Svetlana moved and returned very well," said Kvitova.
"It was tough to come back into the match in the second set. In the third set I was 3-0 down and I didn't think I could still win. I managed to come back on Svetlana's serve and it was a very important moment in the match."
The Czechs' last triumph came when, playing as Czechoslovakia, they beat the former Soviet Union 2-1 in the 1988 final.
Russia, who were without the injured Maria Sharapova and Vera Zvonareva, have won the Fed Cup four times since 2004 and were unbeaten at home in 10 ties since losing to France in the semi-finals in 2003.