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 defense 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.
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Associated Press writer Jovana Gec contributed to this report.