The world number one from Belarus appeared bothered by the high humidity on Pat Rafter Arena in Brisbane, particularly in an error-strewn first set.
But after breaking Mexico's Renata Zarazua at 5-4, the 26-year-old surged through the second set to wrap up the match 6-4, 6-0 in 65 minutes.
"The first match is always a tricky one," Sabalenka said.
"It was a tricky start for me but I'm glad that I closed it out in the first set, and in the second set I felt like whatever I tried to do it would work for me.
"So I'm really happy for the first win of the season."
Sabalenka is bidding to be the first woman since Martina Hingis in 1997-99 to win three Australian Open crowns in succession. The year's opening Grand Slam starts in Melbourne on January 12.
She will play Yulia Putintseva next after the Kazakh's 6-2, 7-5 win over American Mccartney Kessler.
In other matches, Armenia's Elina Avanesyan stunned Spain's fourth seed Paula Badosa in the first match on centre court.
Avanesyan won the first set but when the world number 12 raced back to level the match it seemed like Badosa would progress to the third round.
But the Russian-born Armenian broke early in the decider before easing away to win 6-3, 1-6, 6-2.
There was a second upset when American Ashlyn Krueger downed Russian sixth seed Anna Kalinskaya 6-3, 6-3.
In the men's draw American fourth seed Frances Tiafoe saw off Australian wildcard Adam Walton 7-6 (7/5), 6-3 while Italy's Matteo Arnaldi upset Australian Alexei Popyrin 6-3, 6-2.
