Issues in obtaining a USA visa kept her from defending her Washington DC title. The defending U.S Open champion will have a MRI to assess the damage ahead of the Open kicking off on Tuesday week.
Osaka dropped out of her semifinal match Friday with discomfort in her left knee that caused her worry. She expected to get an MRI. "At times I played some good stuff".
"Last year I won the US Open and this year I'm trying to play the US Open", said Osaka, who secured a second grand slam title at the Australian Open in January.
It's been that kind of week in Cincinnati, with top players in both brackets either struggling or hurt heading into the US Open. She fell to Sofia Kenin right in the opener but by the looks of it, she has made amends for that defeat here.
"I thought she was returning really well today and putting a lot of pressure on me, but I knew I could break back", Keys, the World No. 18, said.
With that, Kenin advanced to the semifinals for the second straight week.
Barty lost the world number one crown to Naomi Osaka following upset losses in her previous two tournaments, but stands to regain her spot at the pinnacle with a Cincinatti Masters final appearance. No. 1 isn't one of them.
Kuznetsova will play for the title on Sunday against the victor of a later semi-final between Americans Sofia Kenin and Madison Keys.
Barty opened the first set strong, opening a 5-2 lead.
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It would not be good to lose three finals in a row, so I'm really happy about this. "I'm really feeling great about my tennis". Medvedev never looked back and he was delighted to win a match he acknowledged would often have slipped away in the past.
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Barty will now unseat Osaka if she advances to the final, having reached the last four with a stunning comeback victory over Maria Sakkari 5-7 6-2 6-0.
"It sucks, especially since I didn't want to get injured this close to the open", Osaka said afterwards.
"That's the beauty of being able to stay alive in the tournament is to give myself an opportunity to keep getting better. But the big picture is NY in 10 days' time".
Barty won the first two games, then lost the set as Kuznetsova, effectively handling the Australian's slices and serving well, won the next six.
She fought off a match point during a three-set win over Anett Kontaveit, showing poise that she'd need to draw on again against Sakkari.
"I don't even really think about winning the tournament", she said. "I'm still able to, more times than not, have the ability to relax and kind of stay clear and come back to what works".
Kuznetsova was delayed in her hardcourt summer start due to U.S. visa problems, but won two rounds last week in Canada before getting her American entry sorted.
On the men's side, qualifier Yoshihito Nishioka withdrew because of illness, sending David Goffin into the semifinals.