The title will be decided on Sunday with two reverse singles and a doubles match at the Olympic Stadium. Kvitova will play Kuznetsova for the first time in reverse singles on Sunday.
Two-time Grand Slam champion Kuznetsova broke Safarova twice in the first set and was leading 5-3 in the second. She clinched the victory on Safarova's serve with a backhand return on her first match point.
Kuznetsova, who is 15-6 in the Fed Cup, said she felt under pressure going into her match, but her experience helped her.
"I stayed focused through the entire match, I served well and aggressively," Kuznetsova said. "I was more on the attack, I was changing rhythm and pace."
Safarova said she didn't play well in the first set but then stepped up her game.
"I didn't catch the beginning of the match," Safarova said. "Sveta played very well in the second set and was not missing, so it was a tough match."
After even play in the first four games, Kvitova dominated Kirilenko with powerful shots from the baseline and frequent volley winners.
"It was much tougher to win today, and I lost much more energy then it may appear looking at the scoreline," Kvitova said.
Kvitova won six consecutive games to take a set and 2-0 lead. Kvitova broke again in the seventh game of the second set and served the match out with an ace.
In the second reverse singles, Kirilenko is expected to play Safarova, with the doubles to follow. However, the matchups are subject to change.
"In the Fed Cup you never know who will oppose you in the reverse singles, but I've won already and do not feel any pressure on my back," Kvitova said.
Kirilenko, whose Fed Cup experience was limited to two matches five years ago, was a surprise choice as Russia's No. 2 for opening singles.
"In the beginning I felt I could overcome her powerful play from the base line," Kirilenko said. "But midway through the first set, Petra added power to her serve, making it tough to return. And I had no chance receiving today, either."
Russia, which is 4-0 in the finals, played without seventh-ranked Vera Zvonareva, who withdrew with a shoulder injury on Friday.
Russia has won the Fed Cup title four times since 2004 and is unbeaten at home in 10 matches since losing to France in the semifinals in 2003. The Czechs are five-time winners, but their last final appearance was in 1988 when, as Czechoslovakia, they beat the Soviet Union 2-1.