The result put the Czechs firmly in the driving seat with Berdych now facing world number two Novak Djokovic in Sunday's opening singles before Stepanek takes on Dusan Lajovic, a late replacement for the injured Janko Tipsarevic, or Bozoljac.
An exhausted Djokovic, who arrived in his hometown after winning four tournaments and 22 matches on the trot before recording a straight-sets victory over Stepanek on Friday, was rested for the doubles.
"Djokovic was totally honest this morning and said that while he was prepared to spend every last ounce of energy in the singles, asking him to play in the doubles too would have been too much," Serbia captain Bogdan Obradovic told a news conference.
"These two guys beat some really good teams, including the Bryan brothers (in the quarter-final win over the U.S.), so putting them together was a logical choice given the circumstances and we have no regrets at all.
"We've been here many times before and if Djokovic beats Berdych to level the score we are confident we can clinch it in the fifth rubber although we are in a very tough situation," added Obradovic.
Berdych and Stepanek improved their Davis Cup doubles record as a pair to 14-1 with an effervescent performance in the packed Kombank Arena, with several hundred colourful Czech fans often gaining the upper hand over 15,000 home supporters in terms of noise.
The away contingent let off their loud horns and danced to the tunes of a Serbian brass-band brought in to put some wind in the home team's sails.
Volleying past their opponents almost at will and carving them open with passing shots time and again, the Czech duo broke both Zimonjic's and Bozoljac's serve in the opening set as the Serbians also committed too many unforced errors.
With the flat-looking Zimonjic dropping his serve again in the opening game of the second set, the visitors comfortably held on to their advantage as Stepanek ran both Serbs ragged with devastating forays to the net.
The Czechs faced their only break point of the match in the fifth game of the third set but Stepanek held serve after a pair of audacious volleys and the champions then stormed back from a 3-1 deficit in the tiebreak to seal victory in two hours 12 minutes.
"We complement each other on the court and that's why we work well in the doubles," said Stepanek.
"This is one of the best Davis Cup doubles matches I've ever played but a lot of the credit goes to Berdych and our fantastic fans who sacrifice so much to follow us around the world and are an unofficial team member.
"We are in a good position to retain the title but we have to stay humble and focused because we face two difficult singles tomorrow."
Should Djokovic redress the balance on Sunday, Obradovic faces another painful selection dilemma as he prepares to choose between Bozoljac and Lajovic who was brushed aside by Berdych on Friday.
"We have to sit down and see what the best course of action is," said Serbia's captain.
"I will talk to the entire squad and make a decision but obviously our first priority is to keep the tie alive and we certainly can't take for granted that Djokovic will beat a player of Berdych's quality."
The Serbs fought back from 2-1 down in the 2010 semis against the Czechs, in the final against France when they won their maiden Davis Cup title and in this year's semis against Canada, each time in the imposing Kombank Arena.
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