Australia bounced again from Wednesday’s Davis Cup defeat by Nice Britain to return from behind and beat France 2-1.
However Alex de Minaur beat Ugo Humbert 7-6 (7-2) 6-3 earlier than Purcell and Matt Ebden received the deciding doubles rubber 7-5 6-3 for final 12 months’s runners-up.
That stored alive Australia’s hopes of qualifying from Group B for the quarter-finals in Malaga in November.
Nice Britain face Switzerland of their second group match on Friday, with qualification for the final eight set to go right down to the hosts’ remaining recreation with France on Sunday.
Defending champions Canada cruised previous Sweden for a second straight Group A win in Bologna, regardless of being with out Felix Auger-Aliassime, Milos Raonic and Denis Shapovalov.
In the meantime, the United States suffered their first defeat in Group D, shedding to the Netherlands in Cut up.
The Czech Republic backed up their Group C win over Spain by defeating South Korea in Valencia, however world primary Novak Djokovic may return to motion for Serbia in opposition to hosts Spain on Friday.