The 110th-ranked Dutchwoman put up a valiant fight and had world number one Williams, who struggled with her serve, on the ropes in the opening set.
Williams, who registered eight double faults in the set, was down a break with Bertens serving for the set when the top seed broke the Dutchwoman in the 10th game to draw level at 5-5 and take it to a tiebreaker.
Williams fell behind 4-0 in the tiebreaker but roared back with five consecutive points and claimed the decider 7-5.
"I never stop. I keep going and give the best effort that I can," Williams said after raising her 2015 match record to 50-2.
Should Williams win her fourth consecutive U.S. Open, the 33-year-old American would become the fourth woman to sweep all four grand slam singles title in one season following Maureen Connolly (1953), Margaret Court (1970) and Steffi Graf (1988).
Williams next faces Bethanie Mattek-Sands, who beat fellow American CoCo Vandeweghe in straight sets in her second-round match.
(Reporting by Larry Fine; Editing by Frank Pingue)
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