Oskaka won her first Grand Slam in New York in September but the match was marred by an on-court argument between Williams and the chair umpire.

The American beat Ekaterina Alexandrova 7-5 6-4 in Toronto, while Japan's Osaka won 7-6 (7-4) 6-4 against Iga Swiatek.

"I've actually been looking forward to playing her," said Williams.

Of 21-year-old world number two Osaka, who also won the Australian Open in January, she added: "She has had a great year early in the season and she's still doing pretty good."

World number 10 Williams - a three-time Rogers Cup winner - went a double break down early on against Russian Alexandrova, and dropped the first three games before battling back with two breaks of her own.

The 37-year-old 23-time Grand Slam champion went on to wrap up the opening set, though was forced to wait until her fourth set point after spurning her opportunities at 5-4 up.

She once again got off to a poor start in the second set by being broken in the first game but levelled at 3-3 and went on to seal with another break as Alexandrova was made to pay for her 11 double faults in the match.

"She hit really, really hard and she was hitting a lot of winners," said Williams. "So I was just happy that I was able to fight through that."

Meanwhile, defending champion Simona Halep also progressed to the quarter-finals, beating Svetlana Kuznetsova 6-2 6-1 in one hour seven minutes.

Romanian fourth seed Halep, who won her second Grand Slam at Wimbledon in July, will play Czech Marie Bouzkova.

Elsewhere, Czech third seed Karolina Pliskova beat Estonia's Anett Kontaveit 6-3 7-5 to set up a last-eight meeting with Canadian Bianca Andreescu, while Ukraine's Elina Svitolina and American Sofia Kenin also progressed.