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Three-time Grand Slam champion Osaka will meet Jennifer Brady in the title match.
The Czech 25th seed rallied after a lengthy medical timeout in the second set to secure a place in her first Grand Slam semifinal.
World No. 1s Ash Barty and eight-time champion Novak Djokovic will lead the fields at the Grand Slam slated to be held from February 8-21.
Former French Open champion Jelena Ostapenko ousted second seed Karolina Pliskova 6-4, 6-2 in the second round.
Italian teenager Jannik Sinner upset 11th seed David Goffin in a breezy 7-5, 6-0, 6-3 victory on his French Open debut.
Halep raced into a 5-0 lead in the opening set, breaking the defending champion three times and also saved three break points at 0-40 down in the fourth game.
Novak Djokovic was made to work hard by Casper Ruud in blustery conditions.
Defending champion Nadal was stunned by Argentine Diego Schwartzman in the quarterfinals.
Pliskova's exit marked the worst performance by a women's top seed in New York since Simona Halep's opening round defeat in 2018.
Serena shook off some COVID-19 layoff rust to grind out a 7-6(6), 3-6, 7-6(0) win over Arantxa Rus to move into the third round of the Western and Southern Open.