Kvitova, who also won the season-ending WTA Championships title last week in Istanbul and rose to No. 2 in the world, opened Saturday's singles rubbers with a 6-2, 6-2 victory against Maria Kirilenko at Olympic Stadium.
Kuznetsova then followed with a 6-2, 6-3 victory over Lucie Safarova. The two- time Grand Slam champion improved to 22-7 in her career in Fed Cup play, and prevented Russia from falling in an 0-2 hole heading into Sunday's reverse singles.
Saturday's results set up an enticing first rubber on Sunday between Kuznetsova and Kvitova. The high-powered match will be pivotal, and will put either Kirilenko or Safarova in position to clinch the title in Sunday's second singles match.
If the sides are tied, 2-2, after those matches, a doubles showdown will decide the title. That will pit the Russian tandem of Anastasia Pavlyuchenkova and Elena Vesnina against the Czech duo of Lucie Hradecka and Kveta Peschke.
The Russians and Czechs have split four all-time matchups, three of which came in the days of the Soviet Union and Czechoslovakia. In their lone meeting since Russia and the Czech Republic became independent nations, the Russians beat the Czechs 2-1 in Madrid, Spain 10 years ago.
Russia dismantled two-time defending champion Italy 5-0 in the semifinals back in April, and has won four of the last seven Fed Cup titles. It last won in 2008, while the Czech Republic is seeking its first title. The former Czechoslovakia captured the coveted chalice five times, led by all-time great Martina Navratilova.