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The number two seed won 7-6 (10-8) 7-6 (7-3), saving seven set points after going 5-1 down in the first set, before roaring back to take both tie-breaks.
Sabalenka will face Marketa Vondrousova in the quarter-finals, with the Czech having produced a dominant performance in a 6-0 6-4 win against Kaia Kanepi.
"When it's 1-5 down, it's like you have nothing to lose, and you just go for your shots without thinking," Sabalenka said.
"That really helped me to stay in the set, to keep fighting and to keep trying."
Fourth seed Veronika Kudermetova eased through after a 6-4 6-0 victory against Bianca Andreescu, while Marta Kostyuk also advanced with a hard-fought 6-7 (5-7) 6-2 6-3 win over Elena Rybakina.
At the ASB Classic in Auckland, second seed Sloane Stephens is out after falling to Rebeka Masarova.
Having been forced to resume on Wednesday after rain suspended play the previous day, Stephens struggled against her Spanish opponent, eventually losing 6-3 7-6 (7-5).
Fifth seed Wang Xiyu is also out after retiring from her match against Karolina Muchova, but seventh seed Danka Kovinic is through after a simple 6-1 6-4 win against Nao Hibino.
Kovinic will face Lauren Davis next after she overcame Tamara Zidansek 6-2 6-1, while fellow American Sofia Kenin will take on number one seed Coco Gauff in the last 16 after she beat Wang Xinyu in straight sets.