The Australians lost both opening-day singles matches, with spearhead Talia Gibson a shock loser to British teen Mika Stojsavljevic.
Gibson was expected to get the tie at John Cain Arena off to a flying start on Friday, but went down 7-6 (7-4) 7-5 against the lowly-ranked 17-year-old.
Kimberly Birrell was then unable to get the home team back on level pegging, falling 4-6 6-3 6-3 against Harriet Dart.
That leaves experienced pair Storm Hunter and Ellen Perez needing to win the doubles in the opening match on Saturday for Australia to remain alive in the tie.
Stosur felt her team could wrestle back the result, also needing to win the reverse singles to book their place in the Finals in China in September
"I absolutely believe in Storm and Ellen to hopefully get tomorrow's doubles match going in our favour to really make it a real tight tussle," the former US Open champion said.
"It's best of five for a reason so we've got players on our side that all of us believe in, and tomorrow is going to be all about that.
"We're going to have to fight, we're going to have to make it something special, but we're certainly up for the challenge, and I know that we're absolutely capable."
World No.56 Gibson took over as the leading local following injury to Maya Joint and arrived at the tie in sparkling form, having recently beaten five top 20-ranked players and rocketed to her career-high ranking.
With the visitors missing their four best players, the Australians were hot favourites but that was quickly dismissed by big-serving world No.275 Stojsavljevic, who tallied a whopping 12 aces for the match.
"It's my first time playing a match in the Billie Jean King Cup for Team Australia, so there was obviously some nerves out there today and not the way I would have liked to have played and not the result that I would have liked to have had," Perth product Gibson said.
"Credit to Mika, she came out playing really well, served amazing, so I did my best with what I was able to bring today, but unfortunately it wasn't enough."
World No.80 Birrell was on track to level for the Australians, taking the first set, but lost momentum against against the gritty 173-ranked Dart.
The pair exchanged breaks in the third set but Dart broke again to lead 4-3 and wasn't troubled from that point.
Dart will partner Jodie Burrage in Saturday's live doubles match, with the reverse singles scheduled for later in the day.
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