World No 1 Williams, the two-time defending champion, eased past world number 50 Kaia Kanepi, 6-3, 6-3, for a fourth win over the Estonian.
"It's my first quarter-final of the year at the Majors -- at last I did it," said the 32-year-old American, who had fallen in the fourth round in Australia, the third round at Wimbledon and suffered a second round French Open exit.
Italian 11th seed Pennetta, also 32, reached her fifth quarter-final in New York with a 7-5, 6-2 victory over Australian 29th seed Casey Dellacqua.
Pennetta made the semi-finals in 2013, where she was defeated by Victoria Azarenka, but despite having a 5-0 losing record against Williams, she refuses to believe that the outcome of Wednesday's quarter-final is a foregone conclusion.
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"Of course, she's better than me, but I still believe I can beat her. If she doesn't have a good day I can do that," said Pennetta of an opponent who has dropped just 17 games in four rounds so far.
Monday's other fourth round ties will see seventh-seeded Canadian Eugenie Bouchard take on Russian 17th seed Ekaterina Makarova and former world number one Azarenka, the runner-up to Williams in 2012 and 2013, play Serbian qualifier Aleksandra Krunic, ranked at 145.