Ivan Ljubicic, in the unusual dual role of player and captain, inspired Davis Cup champions Croatia to an unassailable 3-0 lead over Austria in the World Group first round on Saturday.
Croatia, who won the trophy for the first time by beating Slovakia in December's final, were joined in the last eight by their next opponents Argentina, France, Russia, Chile and Belarus, who surprisingly knocked out Spain.
Australia, minus the injured Lleyton Hewitt, won Saturday's doubles to go 2-1 up on Switzerland, who are without resting world number one Roger Federer.
The United States also took a 2-1 lead over Romania when Victor Hanescu retired hurt during the doubles.
In Graz, Ljubicic and Mario Ancic roared back from two sets down to beat Julian Knowle and Juergen Melzer 3-6, 3-6, 6-4, 6-4, 8-6.
"We were definitely the stronger team and knew we could win it," Ljubicic told reporters at the end of a four-hour epic. "We did not play too well in the first two sets but then found our rhythm.
"I am number five in the world so I expect to play well. We made some mistakes and it got difficult but we hung in and won it."
Croatia will play Argentina in the quarter-finals in April, the South Americans advancing after David Nalbandian and Agustin Calleri defeated Swedes Jonas Bjorkman and Simon Aspelin 6-2, 7-6, 2-6, 6-4 in Buenos Aires.
Sweden, who won the title seven times between 1975 and 1998, struggled on the clay surface that favoured the home side and had their serve broken 13 times.
"The country to beat now is Croatia," Nalbandian told reporters. "It won't be at all easy."
In Minsk, Max Mirnyi and Vladimir Voltchkov overcame Feliciano Lopez and Fernando Verdasco 7-6, 6-4, 7-5 to earn Belarus an upset win over Spain, champions in 2000 and 2004.
Voltchkov praised the crowd as Belarus maintained their unbeaten home record in the World Group.
"It's our joint win," he said. "Our fans gave us great support. They inspired us so much that we just could not lose today."
Belarus are likely to face Australia in the last eight after doubles specialists Wayne Arthurs and Paul Hanley beat Switzerland's Stanislas Wawrinka and Yves Allegro 7-6, 6-4, 4-6, 7-6 in Geneva.
"We're all feeling pretty good about ourselves right now," said Australia captain John Fitzgerald. "It was one hell of a match."
Germany's return after a two-year absence from the World Group ended in defeat in Halle.
France seized an unbeatable 3-0 lead when Arnaud Clement and Michael Llodra came from a set down to sink Tommy Haas and Alexander Waske 6-7, 6-3, 6-4, 6-1.
Russia will be France's quarter-final opponents after they beat the Netherlands 3-0 in Amsterdam.
Mikhail Youzhny and Igor Andreev won 6-2, 3-6, 6-4, 6-4 against Raemon Sluiter and John van Lottum to delight the Russians, who are without Marat Safin due to a knee injury.
Romania's Hanescu and Horia-Vlad Tecau dropped the first set 6-2 to American brothers Mike and Bob Bryan, the world's top-ranked team.
Hanescu took a timeout after injuring his left side with the score at 4-2 and although he returned he retired hurt at the end of the set.
"It's not sweet but we'll take it," Bob Bryan told reporters.
Chile reached the quarter-finals for the first time since 1982 when Fernando Gonzalez and Nicolas Massu, Olympic champions in 2004, beat Slovakia's Michal Mertinak and Lukas Lacko 6-2, 7-5, 3-6, 6-4 to give their team a 3-0 lead over last year's runners-up.