After the opening day of the tie in Ostrava had been shared 1-1, world number three Karolina Pliskova powered past French Open champion Garbine Muguruza 6-2 6-2 before Barbora Strycova beat Lara Arruabarrena 6-4 6-4.
Strycova dedicated the win to double Wimbledon champion Kvitova who is recovering from a serious hand injury sustained during an attempted robbery at her home late last year.
"Of course we are thinking about her every day and we were talking to her," Strycova said. "Of course this was for her. We hope she comes back and we will welcome her with open arms."
Belarus also reached the semi-finals without the services of their top player Victoria Azarenka, who has just had a baby.
They beat the Netherlands 4-1 with 18-year-old Aryna Sabalenka securing the decisive point on her debut.
They will face Switzerland in the semis after they beat France 3-1. The Czechs are waiting for the winner of the tie between the U.S. and Germany which has been delayed by bad weather. (Reporting by Martyn Herman, editing by Pritha Sarkar)
Read the original article on Eurosport: Czechs make light of Kvitova absence to reach Fed Cup semis