Second seed Bertens took exactly an hour to see off qualifier Ysaline Bonaventure 6-4 6-2, the world number eight dominant on serve throughout the contest.
Sabalenka, who has moved into the WTA’s top 10 for the first time, was similarly impressive as she also overcame a Belgian opponent, beating Alison Van Uytvanck 6-1 6-4.
Next up for Sabalenka is a clash with Ekaterina Alexandrova, who triumphed 7-5 6-2 against fellow qualifier Tereza Martincova.
Bertens, meanwhile, will face Anastasia Pavlyuchenkova after the Russian ousted sixth seed Jelena Ostapenko 6-4 6-4.
At the Thailand Open, Tamara Zidansek came through a remarkable contest with Jennifer Brady.
Zidansek took the first set, lost the second 6-0 and then blew three match points after opening up a 5-1, 40-0 lead in the third.
Brady then failed to convert two match points of her own before Zidansek eventually triumphed 11-9 in a decisive tie-breaker, taking her seventh opportunity to finish a topsy-turvy match.
Magda Linette, Viktorija Golubic and Wang Yafan are also through to the quarter-finals in Hua Hin, the latter benefiting from Zhang Shuai’s retirement through illness.
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