Zahlavova and Hlavackova teamed for a 7-6 (9-7), 6-3 win over Spain's Carla Suarez Navarro and Silvia Soler-Espinosa to complete the seesaw series and advance the Czechs into the Fed Cup semifinals against defending champion Italy.
The doubles match completed a rain-delayed series in which neither side was able to won consecutive matches until the fifth game of the best-of-five quarterfinal.
Spain entered the day with a 1-0 lead but Klara Zakopalova was able to finish off a 6-3, 2-6, 6-1 win over Maria Torro-Flor.
Zakopalova was put into action for the next match but fell 1-6, 6-3, 6-3 to Suarez Navarro. Lucie Safarova, who had been ill, answered for the Czechs with a 6-4, 1-6, 6-3 decision over Soler-Espinoza, leaving the match to be decided in doubles.
The Czechs fought off a pair of set points in the tiebreaker, winning five of the last six points for the advantage. They went ahead with a third-game break but Spain pulled even with a break in the sixth game to get to 3-3.
That, however, would be the last game the Spanish would win as Zahlavova and Hlavackova broke immediately back, held serve and recorded a fifth break to win the series.