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Barty delivered a serving masterclass to reach the last 16 for the second straight year with a clinical 7-5 6-3 victory over rising Greek Maria Sakkari on Saturday (AEST).
Sakkari, seeded 30th, had beaten Barty last year in Indian Wells but Australia's world No.2 played the match on her terms from the outset.
The French Open champion fired down 10 aces and dropped serve only once while breaking Sakkari four times during the 87-minute work-out in Louis Armstrong Stadium.
"This is an incredible court. New York is an incredible city and last year I felt like an adopted American playing with Coco (Vandeweghe) in the doubles, so I'm glad you haven't forgotten," Barty said after enjoying clear crowd favouritism during the match.
"Maria is an incredible competitor, a great mover around the court and plays her best tennis when she's on the move and so it was important for me to try and dictate without going into her patterns.
"It's tricky to play a friend but I was really happy with the way I was able to close out those two sets."
Barty will face 18th seed Qiang Wang next on Monday, with the winner likely to strike Williams in the last eight.
Continuing her relentless quest for a record-equalling 24th grand slam singles title, eighth-seeded Williams swatted aside Karolina Muchova 6-3 6-2 in her third-round match.
Barty and Williams were also slated to collide in the Wimbledon quarter-finals, only for Australia's then-world No.1 to suffer a shock fourth-round loss to unseeded American Alison Riske.
So Barty certainly won't be taking Wang lightly, especially given the Chinese is the highest-ranked rival the second seed has played since downing Madison Keys in the French Open quarter-finals two months and 16 matches ago.
Barty, though, can take comfort from the fact she has beaten the world No.18 Wang in straight sets in their two previous encounters, both last year.
