Rybakina, the 2022 Wimbledon and 2026 Australian Open champion, will meet fourth seed Coco Gauff for a place in the final after the American's opponent, Belinda Bencic, withdrew earlier on Tuesday (local time) with a hip injury.
In the first tour-level meeting between Osaka and Rybakina, the Japanese player looked to be cruising to victory after breaking in the opening game and holding that advantage to pocket the first set.
The four-time grand slam champion then surged to a 4-2 lead in the second set, but Rybakina rallied and came out on top in a tiebreak to force the decider.
In the third set, the Kazakh successfully defended four break points before breaking Osaka's serve in back-to-back games to seize control and seal victory in two hours and 33 minutes.
"This first game of the match was really tough because it cost me the set," Rybakina said.
"In the second I was just trying to stay closer to the score, even if I'm losing.
"It's rare when you don't play some players for so many years you're on tour.
"She's a great champion. She's a fighter. I knew it would be a tough match."
Earlier on Tuesday, Gauff advanced without striking a ball after Bencic withdrew from their quarter-final, giving the American more time to fine-tune her game ahead of the US Open.
The 2023 US Open champion is into the 16th WTA 1000 semi-final of her career as the 22-year-old chases her first title of the year.
Gauff finished runner-up in Miami and Rome, before her Wimbledon campaign ended in a tight semi-final defeat.
She has introduced new tactical elements to her game and has looked strong in Toronto, where she has not dropped a set.
The only previous meeting between Gauff and Rybakina also came in Toronto, where the American won in three sets in 2022.
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