The world number 13, who reached her first Grand Slam quarter-final at her home Australian Open last month, beat Madison Keys and Sofia Kenin in the singles before teaming up with Priscilla Hon in the decisive doubles tie to seal a tense 3-2 win in Asheville, North Carolina.
"It's the best feeling in the world, to be honest," Barty told reporters.
"No matter what the crowd is like, when you're playing with Australia written on your back, wearing the green and gold, it's the best feeling, regardless if you're home or away."
Seven-times champions Australia, bidding for their first title since 1974, sealed their first semi-finals berth since 2014 and will meet Belarus at home in April.
Third seed Belarus, with twice Grand Slam champion Victoria Azarenka playing her first tie in three years, thrashed Germany 4-0, while Romania stunned defending champions Czech Republic 3-2 and will take on France in the other semi-final.
Belarus would present a "very challenging tie", Australian number three Daria Gavrilova said.
"They actually have a really young team, as well," said the world number 47.
"(Aryna) Sabalenka is probably playing her best tennis right now. (Aliaksandra) Sasnovich is right behind her. She's been pretty consistent. They've got Azarenka. She brings the experience to the team.
"But we'll have the home advantage. Hopefully we can get to
the finals."
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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