Serbia, who had been given a flying start by 12-times grand slam champion Novak Djokovic on Friday on his comeback from an elbow injury, completed a 3-0 victory over Spain in Belgrade.
A weakened France also proved too strong for a British team without Andy Murray in Rouen as they too moved into an unassailable position at 3-0.
The U.S. pair of Jack Sock and Steve Johnson kept their country's hopes alive as they beat Australia's Sam Groth and John Peers 3-6 6-3 6-2 2-6 6-3 in Brisbane.
Australia had taken a 2-0 lead on Friday when Jordan Thompson stunned Sock and Nick Kyrgios eased past John Isner.
Belgium were also leading 2-0 after the first day of their tie against Italy in Charleroi but were pegged back as Simone Bolelli and Andreas Seppi clawed out a five-set win against home duo Rubens Bemelmans and Joris de Loore.
Bemelmans and de Loore had a match point to win the tie in the fifth set tiebreak but the Italians nicked it 8-6.
France are in the semi-finals for the fifth time in eight years after Julien Benneteau and Nicolas Mahut beat British duo Jamie Murray and Dominic Inglot 7-6(7) 5-7 7-5 7-5.
It was revenge for France's defeat by Britain in 2015 when Andy Murray inspired his nation to the title.
Serbia's Viktor Troicki and captain Nenad Zimonjic combined to beat Spain's Pablo Carreno Busta and Marc Lopez 4-6 7-6(4) 6-0 4-6 6-2.
It was veteran Zimonjic's 30th Davis Cup doubles win.
"I'm proud of them all. They were amazing the whole week. We had a great atmosphere and worked really hard," Zimonjic said.
France and Serbia faced each other in the 2010 final when Djokovic led his nation to a first title.
Kyrgios has the chance to clinch Australia's place in the semis on Sunday in the opening rubber against Sock, while in Belgium David Goffin can wrap it up for the hosts when he takes on Paolo Lorenzi in the first reverse singles.
(Reporting by Martyn Herman; Editing by Ian Chadband)
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