Roger Federer, the 17-time Grand Slam title winner, and Australian Open champion Stanislas Wawrinka won their reverse singles as Switzerland beat Kazakhstan 3-2 in Geneva.
In their first semi-final since 2003 they will face Italy who defeated Great Britain 3-2 in Naples.
France came back from 2-0 down to see off underdogs Germany 3-2 in Nancy and will face two-time defending champions Czech Republic, who crushed Japan 5-0.
World number four Federer, who had never played a decisive Davis Cup rubber, cruised past world 64 Andrey Golubev 7-6 (7/6), 6-2, 6-3 for the winning point.
Earlier, world number three Wawrinka beat Mikhail Kukushkin, the world 56, 6-7 (4/7), 6-4, 6-4, 6-4 to bring Switzerland level.
It was a much-needed win for Wawrinka who had lost his singles opener to Golubev on Friday and then teamed with Federer in a losing doubles on Saturday.
"I have had two very, very difficult days," admitted Wawrinka.
"I take responsibility for our defeat in the doubles, I didn't do what was necessary."
Federer played in the Swiss team which lost to Australia in the 2003 semi-finals, surrendering a two-sets to love lead against Lleyton Hewitt.
"It was one of my biggest defeats. But I learned a lot and if I have had the career I've had since that time, it was due to matches like that."
Italy foiled Britain's dream of a first semi-final appearance in 33 years with a battling 3-2 quarter-final win on the Naples clay.
The British were in control, leading 2-1 going into Sunday's closing two reverse singles.
Murray and Fognini unwell
But world number 13 Fabio Fognini stunned Wimbledon champion Andy Murray 6-3, 6-3, 6-4 with Andreas Seppi securing the decisive point with a 6-4, 6-3, 6-4 victory over James Ward.
The Italians, who last appeared in the semi-finals in 1998, will now travel to Switzerland in the September 12th -14th showdown.
Murray's defeat to Fognini was the Scot's first Davis Cup singles loss since 2005 and it came three days after he suffered a stomach bug.
"He played very well today, that's for sure," Murray said.
"He's a very good player especially on clay."
Fognini revealed he had been sick three times in the match against Murray.
"Of course I suffered on all three days," said the colourful Italian.
"I think the first day was the worst one because I was not feeling really good," he said.
"Also yesterday during the doubles I started to feel something after two sets and at the end I think we were a little bit unlucky.
"I was really angry after the match and during the night, but this morning I woke up and said 'OK, let's go, put your face in the court like always' and I was right today."
France came back from 2-0 down in the Davis Cup for the fourth time by seeing off a German team lacking their top six players.
Gael Monfils secured the decisive fifth point with a 6-1, 7-6 (7/0), 6-2 win over Peter Gojowczyk after Jo-Wilfried Tsonga had earlier levelled the tie at 2-2 beating Tobias Kamke 6-3, 6-2, 6-4.
"It's incredible," said Monfils.
"This is the first time this has happened for me," he said.
"I was stressed all day but now I am super happy."
In Tokyo, Czechs Lukas Rosol and Jiri Vesely showed no mercy in winning Sunday's dead singles rubbers against Japan.
Rosol beat Yasutaka Uchiyama 6-3, 3-6, 6-4 before left-hander Vesely swept past Taro Daniel 6-4, 6-4.
Czech captain Jaroslav Navratil said his team were capable of capturing a first hat-trick of titles since the United States won the third of five in a row in 1970.
"We have won the trophy the last two years so we have confidence," he told AFP after the visitors reached the semi-finals for the fifth time in the last six years without the services of top player Tomas Berdych.