The teams were locked at 1-1 after Friday's opening singles, with Djokovic beating Stepanek in straight sets before Berdych redressed the balance against late replacement Dusan Lajovic, who stepped in for the injured Janko Tipsarevic.
Djokovic faces Berdych in Sunday's opening reverse singles before world number 117 Lajovic takes on Stepanek in a potentially decisive fifth rubber in the imposing Kombank Arena.
The Czechs are vying to become the first nation to retain the trophy since Spain won back-to-back titles in 2008 and 2009, while hosts Serbia are bidding for their second cup after winning it at the same venue in 2010.
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- Dusan Lajovic