Djokovic beat Radek Stepanek 7-5, 6-1, 6-4 in the first match. Berdych then defeated rookie Dusan Lajovic 6-3, 6-4, 6-3.
With their 13-1 record in Davis Cup doubles, Berdych and Stepanek have a chance to give the Czechs the lead in the best-of-five series Saturday.
The Czechs are in the final for the third time in five years. Serbia won its only Davis Cup title in Belgrade in 2010, beating France.
In the first set, Djokovic broke Stepanek to go up 4-2. Then he had to save two break points in the next game and failed to serve out the set at 5-3, after a series of errors. He broke again, however, in the 12th game to take the lead.
The second-ranked Serb held serve the rest of the match. He saved seven break points, converting five of six he created.
“Whenever I would face (break points) I would come up with some big serves,” Djokovic said. “I think that is what helped me stay confident in those moments.”
Berdych broke once in each of the first two sets, and twice in the third against Lajovic. The 23-year-old Serb has a 5-12 record on the ATP tour. He replaced Janko Tipsarevic, who missed the final with a heel injury.
The Czechs hope for a win in the doubles, as Berdych faces Djokovic in the reverse singles on Sunday.