The seventh seed from Westmount, Que., will next play the unseeded Irina-Camelia Begu of Romania (42nd), who beat Germany's Carina Witthoeft (104th) 6-4, 6-4 later Friday.
Bouchard made her breakthrough in Melbourne a year ago, reaching her first Grand Slam semifinal and duplicating that showing four months later in Paris before playing the Wimbledon final.
The 20-year-old's win over the 36th-ranked Garcia made amends for a loss to the French player last year in Acapulco.
"I wasn't playing great tennis in the first. I feel like she was putting some pressure on me and I really didn't feel like I got a rhythm," said Bouchard. "But I'm happy that I just kept going. Even if it wasn't going so well, I was able to turn it around.
"So, I loosened up a bit and started going for my shots and playing my game, which is what I need to do more. Probably taking a bit of time away from her stepping in."
Though she will not be facing a seed in the next round, Bouchard remains on guard against any potential upset threat in her weekend fourth-round test.
"Every player here is really good. It's the fourth round of a Grand Slam. Anyone you play will be super-tough," she said.
"I'll be ready for a battle, I'll try to play my game and have some fun also."
Bouchard earned her win over Garcia with a performance witnessed by her several-dozen strong singing, chanting Genie Army fans, all wearing matching maple leaf t-shirts.
She finished the match in 78 minutes.
The opening set turned into a struggle for both women, with six breaks of serve.
Bouchard struck a key blow in the marathon sixth game which lasted nearly a quarter of an hour and did not end until Bouchard converted on a seventh break point as Garcia netted a backhand for 3-all.
But moments later, Bouchard was on the back foot after losing serve, only to get it back in the next game and square the set at 4-4.
Bouchard broke in the 12th game to claim the 56-minute set, as Garcia sent a forehand wide.
The momentum completely shifted in the second set as Bouchard suddenly became untouchable, winning the contest on her second match point.
"I just tried to stay calm," Bouchard said. "I knew that I would hopefully find my groove at some point. Kept going, going, tried to stay with her on her service games.
"I was telling myself to be ready for anything and try to get a rhythm even though it was hard. Finally it clicked a little bit and I was able to roll."
In doubles, Canadians suffered back-to-back losses, with veteran Daniel Nestor and Indian Rohan Bopanna taken out by Spain's Feliciano Lopez and Nestor's former partner Max Mirnyi of Belarus 7-5, 6-3.
The last time Nestor lost this early in Australia was 2009. The end came as Bopann put a forehand service return into the net on the first of two Mirnyi match points after 73 minutes.
"There are times when things go your way and times when they go against you," said Nestor. "We played fine here, but every match comes down to a couple of points.
"Had we gotten an early lead it could have all been different."
Vancouver's Vasek Pospisil was evidently feeling the effects of his draining singles win on Thursday as he and Austrian Julien Knowle had to quit after just three games and nine minutes while leading Benjamin Becker of Germany and Artem Sitak of New Zealand 2-1.
Pospisil is due on court in the singles third round on Saturday against Spain's Guillermo Garcia-Lopez.
He was treated on court for various back and hip complaints during his singles win over Italy's Paolo Lorenzi.