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The world number one struggled throughout as her opponent threatened an upset before she eventually prevailed by a 7-6(5) 6-3 scoreline.
Over 100 places separate the two players in the world rankings, but it was Bertens who made the faster start to the contest, immediately breaking the American to cause a few murmurs on Arthur Ashe Stadium.
Bertens held serve until 5-4 to give herself a chance to serve for the set, but Williams mounted a response, breaking to 15 to level the opener.
Bertens took the opening four points of the tie-break to leave Williams in trouble, but the 33-year-old reeled off seven of the next eight points to snatch the first set.
Williams broke serve at the start of the second to suggest that she could run away with the rest of the match, but her opponent had other ideas as she struck back almost immediately.
Bertens couldn't maintain her form, though, and Williams recorded two more breaks of serve to progress through to the last 32, where she will play Bethanie Mattek-Sands.