"It really means a lot," said Osaka, whose interview on the court after the game made him want more to a growing legion of fans.
Osaka celebrated its victory calmly and coldly unlike the floods of tears that greeted its victory by 16 against Aryna Sabalenka.
"I cried a lot the last time and there were a lot of people making fun of me, so this time I went straight to the network.
"I was going crazy inside and my whole body was shaking, but overall I am very proud of not breaking a racket."
Osaka, the daughter of a Japanese mother and Haitian father, said she enjoyed playing in the scorching heat of New York, which has been such an important issue for the tournament.
"I really do not think it's that hot, I'm sorry, I'm used to the heat of Florida.
"I like to sweat."
Osaka eliminated Tsurenko, number 36, in just 57 minutes, as the Ukrainian's challenge failed in a flood of errors.
The 29-year-old, who knocked out the world number two and Australian Open champion, Caroline Wozniacki, in the second round, made 31 unforced errors and took just seven points from the Japanese star's serve.
Osaka broke in the second and sixth games of the first set, which finished in just 24 minutes.
The crisis soon deepened for Tsurenko, who on Monday needed most of the three hours to beat the Czech teenager Marketa Vondrousova in a match in which she almost suffered a collapse due to heat exhaustion.
She was quickly down two more breaks at 4-0 before wasting three break points in the sixth game when Osaka slipped into a maiden semifinal in the Slams.
"I hate matches like this," Tsurenko said. "I was sick and I woke up with a viral infection.
"I did not want to leave since it's a Grand Slam quarter-final match, but she played well."
Keys, second finalist for Sloane Stephens last year, has a 3-0 record over Suárez Navarro in the quarterfinals on Wednesday.
The Spanish seed, Suárez Navarro, playing in her second US Open quarterfinal match, has reached this stage by eliminating the sixth French seed, Caroline Garcia, and former champion Maria Sharapova in the fourth round.