Instead, she dropped the opening set for the third straight match and this time, there was no digging out.
By winning her first hard-court final since the 2017 U.S. Open, she'll be No. 10 when she returns to NY.
The injury has also loosened Osaka's grip on the top ranking, with world number two Ash Barty poised to reclaim it if the Australian makes the final. A victory Saturday would have moved Barty back ahead for the U.S. Open.
"It' sucks, especially since I didn't want to get injured this close to the Open", US Open champion Osaka told reporters. She'll move up to a No. 10 ranking for NY after another gritty showing, breaking Kuznetsova to tie both sets 5-5 and pull them out. She'll face Madison Keys, who beat Venus Williams 6-2, 6-3 to reach the semifinals for the first time. Kuznetsova has come out of nowhere and has beaten enough respectable players this tournament to grab your attention, but this was Keys tournament to lose as long as she's hitting with this much control. "And now I'm kind of anxious a little bit".
French Open champion Barty will play for a place in the final against Russian veteran Svetlana Kuznetsova, who beat third seed Karolina Pliskova 3-6, 7-6 (7/2), 6-3 to end the Czech's chances of claiming the number one ranking next week.
Ashleigh Barty of Australia (R) shakes hands with Svetlana Kuznetsova of Russian Federation after losing in straight sets.
Kuznetsova is playing only her ninth event after missing the start of the season because of a knee injury. "I want to do well in NY and have a good end to the season".
"I don't even really think about winning the tournament". I just want to have the chance to play it. now.
"I'm in the semis for the first time here", she said.
"I tried to play every point and stay in there", Kuznetsova said.
In the men's bracket, Djokovic overcame concerns about his right elbow but couldn't prevail over Medvedev's 14 aces, some of them on 128 miles per hour second serves. "Every day I'm kind of waking up, hoping that everything still feels like it's in one piece and it feels really good".
The bracket in Cincinnati was billed as a reunion of the Big Four - Novak Djokovic, Roger Federer, Rafael Nadal and Andy Murray back together for the first time since January.
Elsewhere in the men's draw, France's Richard Gasquet earned his first Masters 1000 quarter-final victory in six years, defeating Roberto Bautista Agut 7-6 (7/2), 3-6, 6-2.