The four-time Grand Slam champion needed 2hr 2min to see off the unseeded Russia-born Austrian Potapova 7-6 (7/4), 7-6 (9/7) as the temperatures climbed on Rod Laver Arena.
It set up a clash with fast-rising Canadian teenager Victoria Mboko for a place in the quarter-finals after the 17th seed battled past Danish 14th seed Clare Tauson in three sets.
“I was always on my the back foot, and to be honest, there’s days where you just have to be there, just have to fight and try your best to put the ball back on that side,” said Sabalenka, who was stunned in the final 12 months ago by Madison Keys.
“Even though emotionally I was all over the place, I was able to still fight for every point. It was such a fight, and I really enjoyed it.”
While safely through, Sabalenka will need to sharpen up to go all the way again, with 44 unforced errors, to Potapova’s 25, a blot on the victory.
Potapova had never gone beyond the third round in seven previous tournament appearances and never beaten a world No 1.
But she showed no signs of nerves against the Belarusian, who is chasing a third Melbourne crown in four years.
Both players were broken in their first service games as they felt their way into a contest marked by heavy groundstrokes.
Little separated them until the 12th game when Sabalenka turned up the heat to work four set points on Potapova’s serve.
But the gritty Potapova saved them all and held on to take the set to a tiebreak, where Sabalenka finally took charge.
It sparked her to life and she crunched winners to break Potapova twice and open a 3-0 lead in the second set with the Austrian seemingly out of ideas.
Sabalenka looked destined for a quick finish, but Potaova found a second wind and against the odds broke twice to level at 4-4 and frustrate the top seed.
Sabalenka responded to break back, but lost focus serving for the match and let an unrelenting Potapova back in to send it to another tiebreak.
Showing champion spirit, the Belarusian saved four set points before finally seeing off the Austrian to bank a testing win.