The top-seeded American took a short while to get accustomed to breezy conditions on Arthur Ashe Stadium court before winning 10 of the last 11 games in a 69-minute rout.
Williams, 31, has dropped just four games in four sets at Flushing Meadows this year, slamming the door on the 77th-ranked Voskoboeva by limiting her to nine points in the second set.
The world number one will next meet Voskoboeva's compatriot Yaroslava Shvedova, a 6-2 6-3 winner against Patricia Mayr-Achleitner of Austria.
(Reporting by Larry Fine; Editing by Frank Pingue)
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