Australian Open champion Angelique Kerber lost her singles rubber against Belinda Bencic as Switzerland beat Germany 3-2 to progress to the Fed Cup semi-finals for the first time in 18 years.
The two nations were tied at 1-1 following Saturday's play, with Kerber and Bencic having won a rubber apiece, but it was the Swiss world number 11 who came out on top when the players met on Sunday, winning 7-6 (7-4) 6-3.
Annika Beck levelled the tie by beating Timea Bacsinszky 7-5 6-4, but Bencic teamed up with Martina Hingis to put the match to bed with a straight-sets doubles victory over Andrea Petkovic and Anna-Lena Groenefeld.
Discussing her costly defeat in Leipzig, Kerber commented: "Of course I was a little bit tired, especially at the end of the first set, but I was trying to take all my energy from the crowd and my team.
"Belinda played very solid at the end and well done to her. Today I gave all I had left."
Germany will now meet the Czech Republic, after the defending champions triumphed 3-2 over Romania to register their 100th Fed Cup victory.
Wins for Simona Halep and Karolina Pliskova forced the tie to a doubles decider - Pliskova joining Barbora Strycova to see off Andreea Mitu and Raluca Olaru.
Netherlands completed their stunning victory over Russia with two matches to spare, finishing as 3-1 victors after Kiki Bertens' 6-1 6-4 win against Svetlana Kuznetsova.
"This is unbelievable. I don't think anyone expected that we could win this tie, perhaps we even didn't. It's an unbelievable feeling," said Bertens after guiding the Dutch team to the last four for the first time since 1997.
Russia did salvage some pride with victory in the doubles dead rubber, which Maria Sharapova sat out in order to rest a forearm injury.
France overcame an early blip to seal a convincing 4-1 win over Italy to knock them out for the second year running in the first round.
Camila Giorgi had put Italy in front on Saturday but was on the receiving end of a 6-3 6-4 defeat to Caroline Garcia as France booked a semi-final clash with Netherlands.