Great Britain must beat France in Manchester on Sunday to reach the Final Eight of the Davis Cup.
Leon Smith’s British side would have advanced on Saturday without playing if Switzerland had beaten Australia.
However, Australia won 3-0 as Thanasi Kokkinakis and Alex de Minaur gained singles victories over Dominic Stricker and Marc-Andrea Huesler respectively.
Matthew Ebden and Max Purcell then beat Stricker and Huesler 6-2 6-4 in doubles to secure Australia’s qualification.
The Australian team, runners-up in 2022, would have been facing elimination if they had lost 3-0 to Switzerland, but Kokkinakis beat Stricker 6-3 7-5 before De Minaur triumphed 6-4 6-3 against Huesler.
Ebden and Purcell, who won the men’s doubles competition at Wimbledon in 2022, then produced a dominate display to take Australia to the Davis Cup knockout stages, which will be played in Malaga, Spain between 21-26 November.
‘We need a full house and a lot of noise’
“It’s a massive match. It will go down to the wire – we need a full house and a lot of noise,” said Smith.
A loss would mean Britain, who last won the Davis Cup in 2015, miss out on the closing stages of the tournament.
The match between Great Britain and France will be shown live on the BBC iPlayer and BBC Sport website from 13:00 BST on Sunday.
Holders Canada book Final Eight spot
Elsewhere in the Davis Cup on Saturday, Canada – top of Group A with two wins from two – secured their place in the Final Eight as Alexis Galarneau won the opening singles match with a 6-3 7-6 (7-5) triumph over Alejandro Tabilo of Chile.
In Group C, the Czech Republic secured top spot with their third victory as they beat already-qualified Serbia in Valencia, Spain.
Eighteen-year-old Jakub Mensik beat Dusan Lusovic 6-3 6-2 and Jiri Lehecka won 7-6 (9-7) 7-5 against Laslo Djere of Serbia.
The United States and Finland have both won one and lost one of their Group D matches, and the winner of that tie, staged in Croatia, will qualify.
Finland took a dramatic opener as Otto Virtanen saved two match points in his 7-6 (7-5) 1-6 7-6 (9-7) victory over Mackenzie McDonald.