Barty, who won both her singles matches in the semi-final tie, and veteran Samantha Stosur beat Victoria Azarenka and Aryna Sabalenka 7-5, 3-6, 6-2 in the deciding doubles to set up a final against France in November.
Australia, who have not won the title since 1974, will host the final against the victor of the second semi-final, which was locked at 1-1 in Rouen.
A tight second set also went with serve until the fifth game, and in a mirror image of the first Barty again broke when Sabalenka double faulted as the pressure mounted and sealed the match with an ace.
Barty had some trouble in the first set against the two-time Australian Open champion and saved three break points at 5-5 to go on to win 7-6 (2) 6-3 and level the tie at 1-1. "I stuck to my game plan well and was able to execute under pressure", said Barty.
Australia's last Fed Cup finals appearance was in 1993, while Evonne Goolagong Cawley played the role of spearhead when they last tasted victory 45 years ago.
Now Stosur and the team face another challenge, with the decider against France to be played on home soil in November.
It was the first Fed Cup meeting between the countries.
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Halep had earlier fought back from a set down to beat Garcia 6-7 (6), 6-3, 6-4 in the first of the day's rubbers.
It extended her Fed Cup winning streak in singles and doubles to 14 and she became the first women to win all six matches across two ties on the way to a decider.
The knock on Stosur has always been that she struggles in front of Australian crowds, as she has been unable to get out of the first round of the Australian Open in her last four outings and never made it past the fourth round, despite a career-high ranking of four.
Nerves were fluttering as her match got under way with both players losing their opening service game.
That followed another clinic from Barty, who swept aside world No.10 Sabalenka 6-2 6-2 in another commanding performance less than an hour down the road from her Ipswich home.
World number nine Barty was flawless all weekend, winning both her singles matches against Sabalenka and Azarenka in straight sets before lining up in the doubles, and she needed to be.
But the big-hitting Sabalenka immediately broke back before serving problems cost her again when she sent down two consecutive double faults to once more hand Stosur the advantage.