The world No.1-ranked Barty beat Garcia in just 56 minutes on an outdoor hard court at Perth Arena to get Australia back on track after Kristina Mladenovic beat Ajla Tomljanovic, who was making her Fed Cup debut, 6-1, 6-1 to give France the early lead.
Barty, who won her first singles major at the French Open this year, extended her Fed Cup winning streak to 15 matches, a run that began in February 2017.
"I think that's probably the best tennis match I've ever played in my life," she said. "I could not have asked for a more perfect match."
Barty is set to face Mladenovic in the first reverse singles match Sunday.
"I know she has the weapons to make me uncomfortable," she said of Mladenovic. "It's about trying to nullify that the best I can."
Fresh off her record $4.42 million triumph at the WTA Finals in Shenzhen, China, last weekend, Barty overwhelmed world No. 45 Garcia with potent serving and pinpoint shot-making. She finished with 15 winners and eight aces.
Garcia struggled in the sweltering conditions with the temperature hitting near 40 degrees Celsius (104 Fahrenheit) on the opening day. She hit just three winners in her error-strewn performance.
"She didn't leave me a lot of space. She played well from the first point," Garcia said. "I was disappointed with my performance."
Australia's hopes of ending a 45-year Fed Cup drought started poorly when Mladenovic beat Tomljanovic in 72 minutes.
No. 51 Tomljanovic was chosen over former US Open champion Samantha Stosur as Australia's second singles player behind Barty.
The 26-year-old, Croatia-born Tomljanovic received clearance from the International Tennis Federation to represent her adopted country only last month.
She was broken six times and recorded just two winners for the match.
"It's a tough task for Ajla playing straightaway in the final," Mladenovic said. "I almost played a perfect match. I was really in the zone."
Tomljanovic admitted she struggled with nerves: "I wish I could have done better in the circumstances. It didn't go as planned," she said. "It's really unique. You're not playing for yourself, you're playing for your country and teammates."
The Australian finally held serve on her seventh attempt, but it only slightly delayed Mladenovic's inevitable victory.
Australia hasn't won the Fed Cup, then known as the Federation Cup, since 1974, when Evonne Goolagong, Dianne Fromholtz and Janet Young defeated the United States 2-1 in Italy.
France previously won the Fed Cup in 2003 and most recently made the final in 2016.
The final could well go to the doubles match, when Barty and Stosur will play Mladenovic and Garcia.
Both Barty and Stosur and Mladenovic and Garcia won three-set live fifth doubles matches in April's semifinals to send their countries to the final. Australia beat Belarus in the semifinals and France defeated Romania.