Defending champions the Czech Republic set up a Fed Cup semi-final against Switzerland after battling past Romania 3-2 on Sunday.
The doubles were also decisive for the Swiss, who triumphed over Germany 3-2 despite the hosts fielding new Australian Open champion Angelique Kerber in the singles.
The Czechs won through in the World Group first round tie thanks to Karolina Pliskova and Barbora Strycova defeating Andreea Mitu and Raluca Olaru 6-2, 6-3.
Home team Romania had taken the lead on the day when Simona Halep got the better of Petra Kvitova 6-4, 3-6, 6-3 but the Czechs pulled level at 2-2 after Pliskova beat Monica Niculescu 6-4, 4-6, 6-3 in Cluj.
In Leipzig, Kerber was defeated 7-6 (4), 6-3 by 18-year-old Belinda Belic as the Swiss went 2-1 up but Annika Beck defeated Timea Bacsinszky 7-5, 6-4 to take the tie to the deciding doubles rubber.
Martina Hingis and Bencic then wrapped up Switzerland's progression in the women's version of the Davis Cup with a 6-3 6-2 win over Andrea Petkovic and Anna-Lena Groenefeld.
Bencic had defeated Petkovic 6-3, 6-4 and Kerber overcame Bacsinszky 6-1, 6-3 on Saturday.
"At a certain point my batteries were gone," Kerber, who has had a whirlwind few days after triumphing in Melbourne last Saturday and flying home, told Sat.1 TV. "You just reach your physical limit."
The Netherlands booked a last-four place with a surprise victory over last year's finalists Russia in Moscow.
The Dutch took an unassailable 3-0 lead when Kiki Bertens beat Svetlana Kuznetsova 6-1, 6-4 in the first reverse singles match.
Ekaterina Makarova and Darya Kasatkina defeated Dutch duo Cindy Burger and Arantxa Rus 6-0, 6-2 to make it 3-1 with the second reverse singles cancelled.
The Dutch will next play France in April after the hosts clinched a semi-final place when they beat Italy 4-1 in Marseille.