Kazakhstan had never before qualified for the World Group draw, and Golubev made its first match memorable with a 7-6 (7-4), 6-7 (3-7), 1-6, 7-4 (7-4), 6-3 win over Jan Hajek.
Berdych's answer was a 7-6 (7-5), 6-2, 6-3 victory over Mikhail Kukushkin.
That means Saturday's doubles match -- in which Czechs Lukas Dlouhy and Jiri Vesely square off against Kazakhs Evgeny Korolev and Yuro Schukin -- will play an important role in determine which team moves into the Davis Cup quarterfinals.
No matter who wins Saturday, the series will be decided in Sunday's reverse singles when Friday's winners -- Berdych and Golubev -- play the first match and Hajek and Kukushkin meet in the fifth match of the series.
Berdych lost his serve just once in wining Friday. He had 13 aces among his 46 winners and just 29 unforced errors.
Both Golubev and Hajek managed just two service breaks over the course of their 3 1/2-hour match. But both of Golubev's came in the final set and he lost only three points on serve to make the breaks stand up.
The Czech Republic-Kazakhstan winner will take on the winner of a first-round series between Argentina and Romania in the quarterfinals in July. Argentina is up 2-0 in that series.
Swim Week Miami Beach 2014 [PHOTOS]