Croatia and Slovakia both reached the Davis Cup final for the first time with surprise victories over Russia and Argentina respectively.
Ivan Ljubicic was the hero for Croatia, adding the clinching win over Nikolay Davydenko to his triumphs in the opening singles and the doubles.
Slovakia's win was confirmed when Dominik Hrbaty beat Guillermo Coria to give them an unassailable 3-1 lead.
The final will be played in Slovakia at the beginning of December.
"A greater sports event than the Davis Cup final has not yet taken place in Slovakia," said Hrbaty, who shaved his head along with his team-mates to celebrate.
"I think it can be compared with the soccer World Cup."
The final is likely to be played in the National Tennis Centre in Bratislava, even though its capacity is just 4,000.
Slovakia has a population of 5.4m and gained independence 12 years ago, while Croatia began playing Davis Cup only a year earlier in 1993 following the break-up of Yugoslavia.
"I always thought my Olympic bronze medal was the highlight of my career, but this is better," said Ljubicic, whose 6-3 7-6 (8-6) 6-4 win over Davydenko was his 11 straight victory in the Davis Cup.
"It is phenomenal, unbelievable. It is such a hard path to get this far, to get this high, to get a chance to win the Davis Cup."
Those results include wins over Andre Agassi and Andy Roddick as his side upset the United States out in the first round.
Ljubicic came back from 3-0 and 5-3 down in the second-set tie-break to take a two-set lead and then broke Davydenko to love as he served at 4-5 in the third set to seal victory.
Dmitry Tursunov claimed the dead rubber against Ivo Karlovic 6-4 6-4 to narrow the final margin to 3-2.
Hrbaty described the atmosphere in Slovakia's win as "the best I've ever played in".
"All the people were cheering for me, and I didn't want to disappoint them," he said.
"I played really well right up to the last point, and I'm really happy for my team-mates and all the people."
In the play-offs, the United States, Spain, Germany and Austria won their ties to join Switzerland and Chile, who wrapped up victory on Saturday, in qualifying for next year's World Group.
Andy Roddick needed four and a half hours to beat Belgium's Olivier Rochus 6-7 (4-7) 7-6 (7-4) 7-6 (7-5) 4-6 6-3 in the first reverse singles to give the United States the point they needed.
James Blake made it 4-1 for the US by beating Steve Darcis 7-5 6-1.
Spain, the 2004 champions, held on for a 3-2 win after Juan Carlos Ferrero beat Italy's Daniele Bracciali 6-3 6-0 6-3.
The tie was level at 2-2 after Rafael Nadal beat Andreas Seppi 6-1 6-2 5-7 6-4 in the first reverse singles at Torre del Greco.
Germany beat the Czech Republic 3-2 at Liberec when Tommy Haas beat Tomas Zib 6-7 (3-7) 7-5 6-2 6-0 in the deciding fifth rubber.
Latest Davis Cup World Group play-off standings:
Austria 4-1 Ecuador
Jurgen Melzer (Aut) bt Nicolas Lapentti 6-1 6-0 6-2 (Ecu)
Stefan Koubek (Aut) bt Carlos Avellan (Ecu) 6-3 6-2
Czech Republic 2-3 Germany
Tomas Berdych (Cze) bt Nicolas Kiefer (Ger) 6-7 (5-7) 6-3 2-6 6-4 7-5
Tommy Haas (Ger) bt Tomas Zib (Cze) 6-7 (3-7) 7-5 6-2 6-0
Italy 2-3 Spain
Rafael Nadal (Sp) bt Andreas Seppi (It) 6-1 6-2 5-7 6-4
Juan Carlos Ferrero (Sp) bt Daniele Bracciali (It) 6-3 6-0 6-3
India 1-3 Sweden
Thomas Johansson (Swe) bt Prakash Amritraj (Ind) 6-4 6-3 6-2
Switzerland 5-0 Britain
George Bastl (Swi) bt David Sherwood (GB) 6-3 6-0
Stanislas Wawrinka (Swi) bt Alan Mackin (GB) 7-5 7-6 (7-5)
Belgium 1-4 US
Andy Roddick (US) bt Olivier Rochus (Bel) 6-7 (4-7) 7-6 (7-4) 7-6 (7-5) 4-6 6-3
James Blake (US) bt Steve Darcis (Bel) 7-5 6-1
Chile 5-0 Pakistan
Paul Capdeville (Chi) bt Shahzad Khan (Pak) 6-0 6-1
Adrian Garcia (Chi) bt Aqeel Khan (Pak) 6-2 6-4
Canada 3-2 Belarus
Max Mirnyi (Blr) bt Frank Dancevic (Can) 4-6 6-3 6-4 3-6 6-4
Daniel Nestor/Frederic Niemeyer (Can) bt Max Mirnyi/Vladimir Voltchkov (Blr) 7-5 6-2 3-6 7-6
Vladimir Voltchkov (Blr) bt Frederic Niemeyer (Can) 6-2 6-7 (2-7) 6-3 6-4