The world number one, who is chasing a third Melbourne crown in four years, faces Anastasia Pavlyuchenkova of Russia or Chinese qualifier Bai Zhuoxuan next.
"I did not start my best but she was playing great, it was a tricky start," said Sabalenka, who lost last year's final.
The 27-year-old Belarusian, fresh from winning the season-opening Brisbane International, made a sloppy start in losing the first three points of the match when serving.
In front of the watching Roger Federer, Sabalenka clawed back to deuce but then misfired again to fall a game down in front of a shocked Rod Laver Arena.
Sabalenka, who is the favourite to add a fifth Grand Slam title to her career haul, pulled back level, but if she expected the spirited world number 118 to melt away, it did not immediately happen.
The reigning US Open champion offered an apology to her underdog opponent at 4-4 when she unleashed a forehand into the 20-year-old's head.
Sabalenka's error count was rising, but she finally broke Rakotomanga Rajaonah's resistance to claim the first set, then eased home in the second.
"I was super-happy I found my level," said Sabalenka, who was guilty of 13 unforced errors in the first set.
"It is always tricky playing someone young, someone you don't know, and a lefty (left-hander)."
Sabalenka said she had felt pressure with Federer and Rod Laver watching court-side.
"I hope you guys enjoyed watching me play, I hope you enjoyed it even a little bit," she said in her on-court interview.
"Can I take a picture with you, please?"
Sabalenka was stunned in the Melbourne final by Madison Keys of the United States a year ago.