Twice champion Sabalenka crushed Mboko in a 31-minute first set in the early match at Rod Laver Arena but gave up a 4-1 lead in the second as the 17th seed mounted an impressive comeback.
"What an incredible player for such a young age," the Belarusian said of Mboko, 19.
"It's incredible to see these kids coming up on tour.
"She pushed me really hard today. Super happy with the win ... and happy to be through."
Having been unable to lay a glove on Sabalenka during a seven-game losing streak, Mboko turned the match with a furious attack on the world number one's serve.
Broken twice, Sabalenka had to scrap to take the second set into a tiebreak - but from there she was indomitable.
She charged to a 6-0 lead and sealed the match when a scrambling Mboko sent a forehand sailing over the baseline.
Following her 7-6(4) 7-6(7) win over Anatasia Potapova in the previous match, Sabalenka has now racked up 22 tiebreak wins in succession, including 19 in a row last year.
Few of her rivals have been so consistently present in the second week of Grand Slams.
Sabalenka's next match against 18-year-old American Iva Jovic, who destroyed Kazak Yulia Putintseva 6-0 6-1, will be her 13th consecutive appearance in Grand Slam quarter-finals.
Playing on centre court for the first time at a Grand Slam, Mboko bowed out of her Australian Open main draw debut with her reputation enhanced.
There were no signs she was intimidated by Sabalenka's reputation as she attacked her serve with gusto, forcing her to save two break points in the opening game.
But that was as good as it got for the Canadian in the first set as Sabalenka broke her three times, smacked 15 winners and closed it out with a volley.
Sabalenka rolled on to a 2-0 lead in the second set in a seven-game winning streak before Mboko finally held serve to stem the bleeding.
The Canadian then had the crowd in the palm of her hand as she stormed back into the contest and saved three match points as Sabalenka failed to serve out at 5-4.
While Mboko's returning offensive dismantled Sabalenka's serve, the Belarusian offered the Canadian little credit for it, instead blaming the conditions.
"At some point the sun goes right into your serve point," she said. "It's kind of tricky.
"That's what actually happened. Two breaks that she got, it was on the side when I was facing the sun."
