Djokovic, No. 2 in the world, was dominant in the middle portion of a 7-5, 6-1, 6-4 victory over Radek Stepanek. Berdych, ranked seventh, followed with a solid 6-3, 6-4, 6-3 win against Dusan Lajovic.
The split in the first day of the best-of-five series poses questions for the team captains. Does Serbia use Djokovic in doubles and does the Czech Republic, as it so often has done, go with Berdych and Stepanek in doubles?
Whichever team wins that match will need just one victory Sunday, when Djokovic meets Berdych and Lajovic takes on Stepanek in reverse singles, for the Davis Cup title.
Djokovic had a string in which he won eight of nine games to claim the first two sets against Stepanek. Djokovic won 20-of-22 points in a span in which he took five straight games. The final set turned on a ninth-game break by Djokovic, his fifth of the day, and ended with Djokovic losing only four points over the final three games.
Lajovic, ranked 117th and playing in just his second Davis Cup match, had several games in which he went up 0-30 on Berdych's serve but Berdych never allowed Lajovic a break point.
Berdych was economical on his own break chances. He had one in the first set, breaking serve in the eighth game; two in the second, getting a break in the fifth game; and four in the third, opening the set with the break and closing the match with another.
Serbia is looking for its second Davis Cup championship. It's first, in 2010, is considered the point where Djokovic's game reached its current premier heights.
If the Czechs can win the series, it would be their second consecutive Davis Cup title.
Celebrity Breakups and divorces of 2014 [PHOTOS]