World number two Djokovic raised the volume in the Kombank Arena with a clinical display to beat a stubborn Radek Stepanek 7-5 6-1 6-4 but Berdych was rock-solid in front of a partisan 17,000 crowd as he dispatched gutsy Dusan Lajovic 6-3 6-4 6-3.
Lajovic, a last-minute replacement for the injured Janko Tipsarevic, won the hearts of the home fans with some gritty resistance but the world No. 117 could find no way through against the hard-hitting Berdych.
Saturday's doubles, which is likely to feature Berdych and Djokovic, now looks crucial to the outcome of the tie.
"I am still not sure if I will play in the doubles (on Saturday) because we have to look at Sunday's reverse singles too and the overall exertions of the three-day schedule," Djokovic said after brushing Stepanek aside.
"If selected I will ignore my exhaustion because a full house on a home court brings the out best in me.
"I am not a doubles specialist of course but it's not like I've never played doubles and it also wouldn't be the first time I've been involved in all three Davis Cup days.
"You don't get a chance to play in the final on home court every year so the motivation is huge and I will always be happy to find a way to overcome fatigue after a long season."
Djokovic, who won the ATP World Tour Finals on Monday, beating world number one Rafa Nadal, had to work hard to take the opening set after allowing Stepanek to win three games in a row and level at 5-5.
However, he stepped up a gear to see off the battling Czech to give Serbia the perfect start as they seek to repeat their 2010 victory in the final against France.
"The first set was crucial and after enduring a few poor games I came up with some big serves at crucial moments, especially when I faced break points," Djokovic told a news conference in the same imposing Kombank Arena that staged their momentous triumph three years ago.
"After that I felt pretty much in control of the match."
Stepanek squandered an opportunity to break Djokovic early in the second set and was brushed aside after that as the Serb tormented him with stinging baseline power and trademark winners down the line.
Lajovic delighted the home fans with sporadic moments of inspiration against Berdych, especially with his one-handed backhand down the line.
Five times he had Berdych at 0-30 on his serve only to watch powerless as the world number seven took the next four points to snuff out any danger of a shock.
The colourful band of several hundred Czech supporters celebrated with their noisy trumpets as Berdych closed in on victory. One break was all Berdych needed in the first two sets but he broke twice in the third to see off the 23-year-old.
"It was tough against a player I had never seen play before especially as everyone expected me to bring a point," Berdych said. "He had nothing to lose.
"But I didn't give him any small chance to get me in trouble. But it was not an easy match."
(Editing by Martyn Herman)
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