The duo overpowered the Argentine combination of Leonardo Mayor and Jose Acasuso 6-1, 6-4, 6-3 to give the Czechs a 2-1 lead in the best-of-five match-up.
Berdych improved his record in Davis Cup doubles to 7-0.
Juan Martin del Potro and Berdych are to open Sunday's reverse singles.
Argentina, playing without the injured David Nalbandian, is in the quarterfinals for the eighth consecutive year.
The winner of this quarterfinal match-up will meet the winner between the United States and Croatia in the semifinals in September.
Copyright 2009 by United Press International.