Osaka won her first career Grand Slam at Flushing Meadows but the title match will be remembered for Williams' feud with Carlos Ramos, who warned her for a coaching violation before deducting a point and then a game for her behaviour.
Williams, a three-times Rogers Cup champion, overcame a sluggish start on Thursday to earn a 7-5 6-4 win over Russian qualifier Ekaterina Alexandrova.
Japanese second seed Osaka then closed out the day's action with a 7-6(4) 6-4 win over Polish qualifier Iga Swiatek.
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Williams argues with umpire Carlos Ramos during her match against Naomi Osaka
Image credit: Getty Images
"I've been actually looking forward to playing her for a while," Williams said of the Osaka matchup.
Williams, who is eager to get more hard-court matches under her belt before seeking a record-tying 24th career Grand Slam at the U.S. Open, came back from an early double-break down, helped in part by eight double-faults by Alexandrova in the first set.
The American eighth seed, in her first career meeting with Alexandrova, went down a break again and trailed 3-1 in the second but her serve suddenly started to click as she stormed back to 3-3 and from there raced home.
"She played really well. She didn't really give me any rhythm," Williams said. "I wasn't sure what would come, if it was going to be hard or soft or a winner or what so it was definitely a challenge for me."
Osaka also had her hands full and needed to save a pair of set points before grabbing the opener against Swiatek.
The Japanese made a quick start to the second set and seemed in control until Swiatek made a comeback, the 18-year-old winning over the crowd with her versatile play as the match wore on.
Osaka, 21, said she was excited about the chance to play Williams, someone she grew up watching and has beaten in their two previous meetings.
"Whenever I get the opportunity to play her it's something that I feel is a once-in-a-lifetime opportunity." said Osaka.
"It feels more like I am showcasing my skills to her like 'look what I can do.' So I will go into the match with that mentality."
Defending champion Simona Halep, in her first event since winning last month's Wimbledon, needed 67 minutes to secure a 6-2 6-1 win over Russian wildcard Svetlana Kuznetsova.
Halep took a medical timeout in her previous match to have her left Achilles tended to and she said she still felt pain in the area against Kuznetsova but that it was feeling much better.
"The fact that I'm back in the quarter-finals here means a lot to me," said Halep. "It feels like I'm getting back the rhythm which I had in Wimbledon."
Up next for Halep will be in-form Czech qualifier Marie Bouzkova, who breezed by former French Open champion Jelena Ostapenko 6-2 6-2 and has yet to drop a set.
Earlier on Thursday, Czech third seed Karolina Pliskova beat Estonian Anett Kontaveit 6-3 7-5 to set up a last eight meeting with Canadian Bianca Andreescu, who upset Dutch fifth seed Kiki Bertens 6-1 6-7(7) 6-4.
Also securing passage to the last eight were American Sofia Kenin and 2017 champion Elina Svitolina of Ukraine.
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