The Olympic gold medalist from Switzerland beat Iga Swiatek 7-6 (12), 6-3 to make the last eight in Flushing Meadows for the third time.
Barty will face two-time Cincinnati finalist Angelique Kerber, who won her quarterfinal when Petra Kvitova retired during the second set because of a stomach problem.
The 12th-ranked Bencic beat Elena Rybakina of Kazakhstan 7-6 (2), 4-6, 6-3 on Thursday to reach the gold-medal match at the Tokyo Games.
Bencic struggled with her serve throughout and was broken four times by her Russian rival in 2-6, 2-6 loss.
Keys hit 24 winners against 13 for the sixth-seeded Bencic, who was coming off a loss to Iga Swiatek in the final of the Adelaide International on Saturday.
Bencic was already struggling in the semifinal match with a right leg problem before the end of the first set, which she won.
Third-seeded Bencic broke Pavlyuchenkova in the Russian's first service game in both the second and third sets.
Bianca Andreescu is 33-4 this season after beating No. 13 Belinda Bencic 7-6 (3), 7-5 in Thursday's semifinals.
Naomi Osaka joined 2018 men's champion Novak Djokovic on the sideline before the quarterfinals, exiting with a 7-5, 6-4 loss to the 13th-seeded Belinda Bencic.
Switzerland last won the Hopman Cup in 2001 when Federer teamed with Martina Hingis.
Federer was just 19 when he won the Hopman Cup in 2001 with then top-ranked Martina Hingis.
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