Djokovic overcame some early nerves to beat Radek Stepanek 7-5, 6-1, 6-4 in the first singles match and Berdych then swept past rookie Dusan Lajovic 6-3, 6-4, 6-3 on the indoor hard court at Belgrade Arena.
With their formidable 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. It was still unclear whether Djokovic would play doubles or rest for Sunday's reverse singles.
Djokovic earned his 23rd consecutive victory since losing to Rafael Nadal in the U.S. Open final in September but struggled a bit in the first set. He broke Stepanek to go up 4-2 but had to save two break points in the next game and failed to serve out the set at 5-3, when he committed a series of errors. However, he broke again in the 12th game to take the lead.
"I was a bit nervous in the first set," Djokovic said. "It was very important to win that one against high-quality player like Radek."
The second-ranked Serb held serve the rest of the match — saving seven break points in all, while 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."
Stepanek said Djokovic was serving "tremendously consistently," which prevented him from getting another break.
"The first set was really high quality, and so was the third," the Czech veteran said. "His defence is the best in the world, he proved that with his movement that he showed around the court. He always makes you play an extra shot."
Berdych broke once in each of the first two sets, and twice in the third to wrap up the win 2 hours, 54 minutes against Lajovic. The 23-year-old Serb, who has a 5-12 record on the ATP tour, replaced Janko Tipsarevic, who missed the final with a heel injury.
"It was a tough one, playing the guy I actually saw for the first time on court," Berdych said. "He had nothing to lose. These situations are not easy. I am glad I was able to make it happen in straight sets."
The Czechs will likely need a win in the doubles, as Berdych faces Djokovic in the reverse singles on Sunday.
"When you look at Novak and how he is playing it's like Playstation. So the best way is to unplug electricity."
"I'm happy how I played," Lajovic said. "I'm sure that many of the spectators did not even know how I look like."
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.
Associated Press writer Jovana Gec contributed to this report.