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Serbia, the 2010 winners, reached the last eight for the fourth successive season when Viktor Troicki and Nenad Zimonjic, playing his 18th Davis Cup season, defeated Steve Darcis and Ruben Bemelmans 6-4, 6-4, 5-7, 6-4 to secure a 3-0 win over Belgium.
The Serbs were 2-0 up overnight in Charleroi when Troicki survived a marathon battle to beat David Goffin 1-6, 3-6, 7-6 (7/5), 6-4, 6-4 before world number one and Australian Open title-holder Novak Djokovic eased past Olivier Rochus 6-3, 6-2, 6-2.
"It looks like it was an easy job but it was very tough playing against the Belgian team and in front of thousands of spectators who are cheering for them," said Serbia captain Bogdan Obradovic.
"Still, I want to congratulate my team, they played very good tennis. We went into the second day with lots of positive energy and finally we found the strength to finish the job."
In Rouen, Michael Llodra and Julien Benneteau teamed up to move France into the quarter-finals as they powered past Israeli pairing Dudi Sela and Jonathan Erlich.
The French duo won 7-6 (7/3), 6-1, 6-0 in the doubles to cement an insurmountable 3-0 lead in the tie.
France had led 2-0 overnight in Arnaud Clement's debut as national coach.
Jo-Wilfried Tsonga, the world number eight, beat Amir Weintraub 6-3, 6-3, 4-6, 7-5 before world number 10 Richard Gasquet breezed past Dudi Sela 6-3, 6-2, 6-2.
"What I saw this weekend was fun -- the commitment, level of play," said Clement.
"The richness of this team is to have plenty of opportunities in both singles and doubles on all surfaces."
In Vancouver, Spain were down 2-0 against Canada, a country who have never previously won a World Group clash.
Missing top players Rafael Nadal, David Ferrer, Nicolas Almagro and Fernando Verdasco, the champions in three of the last five years, and runners-up in 2012, were blown off court.
Canadian veteran Frank Dancevic, ranked 166th in the world, stormed to a 6-1, 6-2, 6-2 victory over Marcel Granollers, ranked 34th, to put the hosts up 2-0.
World number 15 Milos Raonic had opened the tie with a 6-7 (5/7), 6-4, 6-4, 6-4 win over Albert Ramos.
Spain, who haven't lost in the first round since 2006, now need Granollers and Marc Lopez to beat Daniel Nestor and Vasek Pospisil in the doubles later Saturday to stay alive in the tie.
"It was beautiful tennis - unfortunately it was painful for us," admitted Spain captain Alex Corretja. "We know it may be a miracle if we want to win this tie."
Canada captain Martin Laurendeau refused to accept that Spain were handicapped by the absence of their marquee names.
"Spain is No.1 in the world, I think Spain could field three Davis Cup teams," he said
In Jacksonville, Florida, Sam Querrey and John Isner powered the United States to a 2-0 lead over Brazil.
Querrey fired 15 aces to beat Thomaz Bellucci 6-3, 6-4, 6-4 before Isner, who missed the Australian Open with a knee injury, pounded 32 aces past Thiago Alves in a 6-3, 7-6 (7/4), 6-3 victory.
Croatia and Italy were level at 1-1 in Turin after Friday's opening day with the winners to meet either Canada or Spain.
Defending champions Czech Republic finished Friday in Geneva at 1-1 against Switzerland. The winners of that tie will meet either Kazakhstan or Austria in the last eight.
Kazakhstan lead 2-1 after the second day in Astana.