Australia battled their way past a determined Brazilian side and a ferocious Florianopolis crowd on Sunday to win a place in the Davis Cup semifinals.
Lleyton Hewitt beat world number two Gustavo Kuerten 7-6 6-3 7-6 to give the 1999 champions a decisive 3-1 lead.
"I feel almost speechless," Hewitt said afterwards. "That's the best I've ever hit the ball."
Australia will now host Sweden in the last four after the Swedes beat Russia 4-1 in Malmo.
France completed the semifinal line-up when they beat Switzerland 3-2 in a thriller in Neuchatel which went to the final set of the final rubber before Nicolas Escude edged George Bastl 1-6 7-5 6-7 6-4 8-6.
Switzerland have never bounced back from a 2-0 deficit in their 72-year Davis Cup history, but hopes were high when Bastl gave them a two-sets-to-one lead in the deciding fifth rubber.
Escude fought back to deny the Swiss, though, and the French team will next travel to the Netherlands after the Dutch brushed aside Germany 4-1 to reach their maiden semifinal.
Two singles players used to sweating it out on the unglamorous Challenger circuit and a doubles pairing of a semi-retired veteran and a slightly injured partner steered the Dutch to the greatest feat in their Davis Cup history.
Few would have put money on a decimated Dutch team finally taming the Germans after former Wimbledon champion Richard Krajicek pulled out with an elbow injury and Sjeng Schalken had to restrict himself to doubles because of a sore foot.
But Paul Haarhuis and Sjeng Schalken beat David Prinosil and Jens Knippschild 6-3 6-4 4-6 6-2 on Saturday to give the Netherlands an unassailable 3-0 lead in Den Bosch.
Nicolas Kiefer won the fifth rubber on Sunday against Jan Siemerink to save Germany from a whitewash but the 4-1 defeat leaves Germany battered.
Tiebreaks were again Brazil's undoing against the team that beat them in last year's semifinals.
Kuerten and Jaime Oncins lost three tiebreaks as they crashed to a straight sets defeat in Saturday's doubles to Hewitt and Patrick Rafter, and Kuerten lost two more on Sunday.
Hewitt, who also beat Fernando Meligeni on Friday, completed his three rubbers without losing a set.
Sweden had their semifinals spot wrapped up by Saturday evening when they took an unbeatable 3-0 lead over a depleted Russian side.
Top-ranked doubles player Jonas Bjorkman partnered Davis Cup novice Simon Aspelin to beat Yevgeny Kafelnikov and Andrei Olhovskiy 4-6 6-1 7-5 6-7 6-2 in a three hour and 20 minute thriller.
"This afternoon was the best I've ever experienced," said Aspelin, a 26-year-old who came from nowhere to reach the semifinals in the ATP World Doubles Championships in Bangalore last December and was summoned to the Swedish squad when Bjorkman's regular Davis Cup doubles partner Nicklas Kulti was forced out with a sore foot.
The victory - whose foundation laid by Thomas Johansson and Magnus Norman who won the two opening singles on Friday - puts Sweden into the Davis Cup semifinals for the 23rd time since 1946.
Russia were missing U.S. Open champion Marat Safin, the world number one in the ATP Entry System rankings, due to injury.
The Swedes ran out 4-1 winners, Norman losing a meaningless fifth dead rubber to Andrei Stolyarov.
The semifinals will take place in September.