Up next up for Osaka will be the victor of the evening match between 2017 runner-up Madison Keys, who at 14 is the highest seed left in the women's draw, and Spain's Carla Suarez Navarro.
It was odd to note that Sevastova, at 18 in the world, is ranked eight places above Williams, but the American - like her friend Tiger Woods - is climbing back to her best.
In the 2018 US Open championship final, Williams will face the victor of the second semifinal between last year's finalist Madison Keys of the United States, the No.14 seed, and first-time Grand Slam semifinalist Naomi Osaka of Japan, the No.20 seed.
"To break in both sets, having solid games there, was really important tonight", Keys said in her on-court post-match interview.
Cilic started better, and was clinically efficient in the opener, breaking Nishikori with his only two opportunities to take the lead. After a quick hold for 2-1, the American maneuvered through a close game to break Sevastova for 2-2 on her third break point, leveling the set at 2-2 after Sevastova pushed a backhand drop shot, her signature shot, into the net. But she does cover the court incredibly well and is amongst the hardest players in the sport to hit through.
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The 20th-seeded Osaka, who won her first career title only in March this year at Indian Wells, had reached the fourth round of Australian Open earlier this year, which was her highest showing at a Grand Slam till Wednesday.
The next obstacle standing between Williams and a ninth trip to the final is rejuvenated Latvian Anastasija Sevastova in Thursday's first semi-final at the Arthur Ashe Stadium, before Osaka faces 2017 runner-up Madison Keys.
Osaka beat her opponent Lesia Tsurenko 6-1, 6-1.
It was a great day for Japanese tennis as both Kei Nishikori and Naomi Osaka booked their passage to the US Open semifinals in two very different matches.
Osaka said: "This moment means a lot". I'm really looking forward to the rest of the year and next year.
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Given the delicate political situation at Old Trafford, the afternoon was as notable for events off the field as on it. Mourinho ended the game going close up to United's traveling support to show his appreciation for their backing.
Only once previously in the professional era, which began in 1968, did Japan have a men's and women's player in the quarterfinals at the same tournament.
The 20-year-old said she was nervous and claimed to be "freaking out inside", though it certainly never showed. "My entire body was shaking, but I was really glad I was able to play well today".
She won 59 points to just 28 for the unseeded Ukrainian, who knocked off No. 2 seed Caroline Wozniacki in the second round.
But after laboring through the heat in her previous match, Tsurenko said she was sick Wednesday, waking up with a sore throat and not breathing well.
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He also repeated a previous comment criticising the "pathetic" attempt to "smear" those close to the president. Did the president speak to Woodward? The Washington Post published excerpts earlier Tuesday.