Defending champions Czech Republic reached the Fed Cup semi-finals for a ninth successive year by beating Spain and Belarus defeated Netherlands to reach the last four of the World Group for the first time.
The Czechs have won the competition in five of the last six years and their dominance continued as Spain were beaten 3-2 in Ostrava on Sunday.
Karolina Pliskova set the tone at a packed Ostravar Arena, easing to a 6-2 6-2 victory over a struggling Garbine Muguruza in the opening rubber of the day to put the hosts 2-1 up.
Barbora Strycova had the opportunity to seal the tie and sent a partisan crowd into raptures by beating Lara Arruabarrena 6-4 6-4.
Maria Jose Martinez Sanchez and Sara Sorribes Tormo won the final doubles rubber against Lucie Safarova and Katerina Siniakova, but that was scant consolation for Spain.
The United States will face the Czechs in the semi-finals in April after beating Germany 3-0.
It proved to be a miserable weekend for Germany, who were issued with an apology by the United States Tennis Association (USTA) after a national anthem associated with the Nazi era was accidentally sung during the opening ceremony in Hawaii on Saturday.
The USA were 2-0 up without striking a ball on Sunday after the injured Julia Goerges retired from her match against Coco Vandeweghe, who was treated as she struggled with the heat in her rubber against Andrea Petkovic but fought back to win 3-6 6-4 6-0 and end the tie.
Belarus broke new ground to reach their first semi-finals in the top tier, with Aliaksandra Sasnovich winning twice as they beat Netherlands 4-1 in Minsk.
They will host Switzerland, who won by the same margin against France in Geneva thanks to singles wins from Timea Bacsinszky - who also prevailed in the doubles to claim three rubbers in the tie - and Belinda Bencic.