The world number one, fresh from winning the WTA Finals in China, came on court in Perth under pressure after the nervous Tomljanovic was thrashed 6-1, 6-1.
But in searing 38 Celsius (100 Fahrenheit) heat she kept her cool to embarrass a stunned Garcia in a rare double bagel, with the Frenchwoman having no answers to the Barty armoury in front of 13,000 fans.
It left the tie evenly poised at 1-1 ahead of Sunday's reverse singles and a doubles clash if needed, with Australia targeting an eighth title and first in 45 years, while France are seeking a third, their first since 2003.
"This is remarkable, I couldn't have asked for a more perfect match. I think that's the best tennis match I've ever played in my life," said Barty. "I felt like I served really well, made a lot of returns. Most importantly I played the big points well. I really wanted to assert myself and I was able to do that really well today."
The French Open champion, capping a breakthrough season, was imperious, firing down pinpoint first serves and effortlessly pushing Garcia around the court, forcing errors.
She set the tone by breaking Garcia's first service game and there was no way back for a player who was once ranked fourth in the world but has slipped to 45.
Barty wrapped up the first set in 29 minutes and there was no let up as she sent down 11 forehand and four backhand winners.
"I was a little bit stressed today, but not too stressed, and I don't think that was why I didn't play well," said Garcia. "Today she just played a very good match from the first point to the last one."
The ease of Barty's 56-minute win was a huge relief for Australian captain Alicia Molik, whose gamble to play Tomljanovic in singles ahead of veteran Samantha Stosur spectacularly backfired.
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