"Especially after coming from injury", he said, "I think I'm enjoying this challenge".
"Well, it definitely means a lot for me, and I always thought if I were to win a Grand Slam, the first one I'd want to win is the US Open, because I have grown up here", said Osaka who was born in Japan but has lived most of her life in the United States.
Keys, a 23-year-old American who is seeded No. 14, overwhelmed Suarez Navarro with her powerful serve and groundstrokes, building a 22-10 edge in winners.
Sep 5, 2018; New York, NY, USA; Naomi Osaka of Japan faces Lesia Tsurenko of Ukraine in a quarter-final match on day ten of the 2018 U.S. Open tennis tournament at USTA Billie Jean King National Tennis Center.
Nishikori overcame a ferocious comeback from Marin Cilic to prevail in five sets 6-2, 4-6, 7-6, 4-6, 6-4.
Since losing to Cilic in the final back in 2014, this was their first meeting at Flushing Meadows and Nishikori triumphed to make it back-to-back semi-finals for him in NY. "My entire body was shaking, but I was really glad I was able to play well today".
Tsurenko, the only unseeded woman to reach this stage of the tournament, will be playing in her first Grand Slam quarter-final when she kicks off Wednesday's action on what is expected to be another steamy day in NY.
She raced to a 3-0 lead in the first set and then 4-0 in the second against the shaky Tsurenko, who finished with more unforced errors than points in her first major quarterfinal.
Against Tsurenko, Osaka barely broke a sweat, winning, 6-1, 6-1.
For Osaka, her victory is the latest milestone in a watershed year for the 20-year-old who won her first WTA Tour title in Indian Wells, Calif., in March. She is now based in Florida, trains with Bajin at Evert's academy in Boca Raton, and made the decision to play for Japan largely because of financial reasons - the Japanese federation offered more support money than the U.S. Tennis Association.
Now, Osaka is one of those players on TV - and seeing the same experience from the other side is proving to be just as cool.
"I hate matches like this", said Tsurenko.
She dropped only seven points on her serve playing on Arthur Ashe Stadium and needed just 57 minutes to rip through Tsurenko.
This time, Keys will play No. 20 Naomi Osaka on Thursday night for a chance to reach the final again.
Suarez Navarro upset former champion Maria Sharapova in the last round and needs another win to become the first Spanish women to reach the U.S. Open semi-finals since Conchita Martinez in 1996.