Earlier, Wimbledon champion Petra Kvitova prevailed over Svetlana Kuznetsova 4-6 6-2 6-3 in the first match of the day to put the Czechs within a point of claiming their first Fed Cup crown after they split from Slovakia in 1993.
Their last triumph came when, playing as Czechoslovakia, they beat the former Soviet Union 2-1 in the 1988 final.
"It a just great feeling for the whole team. We're all so happy," Czech captain Petr Pala said.
Anastasia Pavlyuchenkova, who replaced Kirilenko for the second reverse singles, had given Russia hope of lifting their fifth Fed Cup trophy since 2004 when she overpowered Czech number two Lucie Safarova 6-2 6-4 to pull the hosts level at 2-2.
But after an early threat from Kirilenko and Vesnina, who only played one doubles match together this year losing in the first round of the Italian Open in May, the outcome was never in doubt as the experienced Czech duo took complete control.
After sealing the first set, Peschke, ranked number two in the world in doubles, and Hradecka broke Vesnina's serve twice in the second, clinching victory on their fourth match point.
The Russians, who had not been beaten in Fed Cup competition on home soil since the 2003 semi-final defeat to France, were gracious in defeat.
"Kvitova was the key to their success," Russia's long-serving captain Shamil Tarpishchev said. "She was just phenomenal."
Tarpishchev's counterpart had a different view.
"Of course, Petra played very well but we needed three points to win so it was the whole team's effort," said Pala.
The hosts suffered a huge blow on Friday when their number one player Vera Zvonareva was ruled out of the two-day tie with a shoulder injury.
"Obviously, the loss of Zvonareva was big. Her injury just threw us off our game plan as it happened on the eve of the final," said Tarpishchev.
In-form Kvitova, who crushed Kirilenko -- a last-minute replacement for Zvonareva -- in straight sets on Saturday, fought back from 0-3 down in the final set to beat Kuznetsova.
After losing the opening set, the tall left-hander, cheered on by a small but vocal band of Czech supporters at Moscow's spacious Olympic indoor arena, raced to a 5-1 lead in the second before levelling the match.
Kuznetsova regained the initiative at the start of the third set, but the fired-up Czech reeled off the next six games for her 12th consecutive victory since last month's China Open.
The world number two also went undefeated indoors for the whole year, recording her 21st victory this season.
"I didn't believe I could win the match trailing 0-3 in the third, but my captain told me that it was only one break and it gave me energy to fight back," Kvitova said.