Initially on Wednesday, it looked like the match might follow a similar storyline from four years ago when seventh-seeded Cilic took the opening set from a sluggish Nishikori.
Nishikori overcame a ferocious comeback from Marin Cilic to prevail in five sets 6-2, 4-6, 7-6, 4-6, 6-4.
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.
She was finally tested in the round of 16, edging past No. 26 Aryna Sabalenka 6-3, 2-6, 6-4 in a little more than 2 hours, but she was back in complete control against Tsurenko, winning 20 of 22 points (91 per cent) on her first serve.
"The quarters was sort of my mental goal, every time I played a Grand Slam", said Osaka.
Osaka, who is just 20 years old, is having a terrific 2018 season.
She won 59 points to just 28 for the unseeded Ukrainian, who knocked off No. 2 seed Caroline Wozniacki in the second round.
Tsurenko didn't appear bothered by the conditions, but whether it was her health or just first-time jitters, she was off from the minute she stepped onto Arthur Ashe Stadium. So far in this Open, she's held opponents scoreless in three sets, and she's dropped only one set thus far.
Keys reached the semifinals at her second consecutive U.S. Open after beating No. 30 Carla Suarez Navarro 6-4, 6-3.
The Japanese stars both advanced to the semi-finals at Flushing Meadows on Thursday (AEST). Keys also lost to Stephens in the French Open semifinals this June.