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Serbia, the 2010 champions, reached the last eight for the fourth successive season when Viktor Troicki and Nenad Zimonjic 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.
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.
In Vancouver, Spain were trailing 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, Spain, 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 told www.daviscup.com.
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.
Marin Cilic gave Croatia the lead over Italy in Turin with a 6-1, 6-7 (6/8), 4-6, 6-3, 6-2 win over Paolo Lorenzi.
But Andreas Seppi pulled the hosts level with a 6-2, 6-7 (2-7), 6-4, 6-4 win over Ivan Dodig.
The winners of that tie will meet either Canada or Spain.
Defending champions Czech Republic finished the day in Geneva at 1-1 against Switzerland.
Stanislas Wawrinka, the Swiss team's number one in the absence of Roger Federer, saw off Lukas Rosol, the shock conqueror of Nadal at Wimbledon last year, 6-4, 6-3, 6-4.
World number six Tomas Berdych then defeated Finland-born Henri Laaksonen 6-3, 6-2, 6-7 (5/7), 6-1.
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 while Argentina took a 2-0 lead over Germany in Buenos Aires.