Stepanek started the series with a 7-6 (7-3), 6-3, 6-2 win over Juan Monaco and Berdych followed with a 6-4, 4-6, 6-3, 6-4 victory over Leonardo Mayer.
That puts the Czechs one win away from a third Davis Cup finals appearance in the last five years. The Czechs dropped the 2009 final to Spain but defeated the Spanish last November in winning the team's first Davis Cup since Czechoslovakia won in 1980.
The Czechs will look to wrap up the series in Saturday's doubles when Lukas Rosol and Jiri Vesely are penciled in to take on the Argentine team of Carlos Berlocq and Horacio Zeballos.
If Berlocq and Zeballos win, the series will be determined Sunday in reverse singles when Berdych meets Monaco and Stepanek goes against Mayer.
The Argentina-Czech Republic winner advances to the Davis Cup final Nov. 15-17 against either Canada or Serbia.
Stepanek pounded out 13 aces and lost his serve three times against Monaco but had a pair of breaks in each set in winning the opener. He won nearly half (45-of-95) of the points when Monaco served,
Mayer was up a break late in the first set only to have Berdych come back. He made a late break stand in the second set but Berdych lost only six points on serve in the third set and 10 in the fourth to seal the win.
2014: The Year in Music [PHOTOS]