The world number five Berdych overcame a touch challenge from Leonardo Mayer, winning 6-4 4-6 6-3 6-4 at the O2 Arena in Prague, where the Czech team lifted the trophy as an independent nation for the first time last year.
Earlier, US Open doubles champion Stepanek cruised to a 7-6(3) 6-3 6-2 win over Juan Monaco, Argentina's top-ranked player in the absence of world number seven Juan Martin Del Potro.
Mayer, the lowest ranked on both teams at 93 in the world and making his first Davis Cup appearance since 2010, matched Berdych's power game early on and levelled the match at one set apiece.
But after the 26-year-old Argentine scored the first point of the third set, Berdych reeled off three straight games.
He broke Mayer in the second game with a backhand and sent down a pair of aces in the third, to move into a comfortable position.
"I was kind of fighting with myself with the rhythm of a bit faster court from the beginning in those first two sets," Berdych said.
"Then I just got the rhythm back and started to serve on the standard that I'm used to and getting some easy points, and that was actually the key to the game...
"We have a 2-0 lead after Friday and that is what we wanted or maybe better. The most important thing is now to get ready for tomorrow," he added in a courtside interview.
The Czechs were playing at home for the first time this season and Stepanek got the crowd fired-up early.
He double faulted twice as he blew the chance to serve out the first set at 6-5 but then regained his composure in the tie-break, storming ahead 6-0, before closing it out with a well-placed backhand to the corner.
Stepanek, who came into the competition on the back of winning the men's doubles title with Leander Paes at Flushing Meadows last weekend, then comfortably saw out the match in straight sets.
"The longer I was on the court, the better my play got," he said after giving the Czechs the perfect start to their semi-final.
With Stepanek winning three times as many points at the net as his opponent, Monaco said the court favoured the Czech.
"I had my chances in the first set but couldn't make them," he said. "He played really well. I knew he was a good player on this type of court. Playing this kind of court is not easy."
Berdych and Stepanek are likely to team up for Saturday's doubles, hoping to finish the job and secure a spot in the final where they will face either Serbia or Canada.
They are Czechs' all-time best doubles pairing with a 12-1 record and helped their country lift the Cup in 2012 for the first time since Czechoslovakia won in 1980.
They played in every live rubber in that title campaign, but are featuring together in a tie for the first time in 2013.
Argentina were runners-up in 2011 but lost to the Czechs at home in the semi-finals last year. They have yet to win the Davis Cup despite four final appearances.
"It is more difficult than yesterday. But we still have three points to play for... We still have a chance," Argentina's captain Martin Jaite said.
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- Leonardo Mayer