Seven-time Grand Slam champion Williams, 37, was winning matches at Indian Wells previously Kasatkina had even been conceived, however was exhausted by the adolescent, who broke her seven times.
After the combine exchanged the opening two sets, Williams squeezed out a 5-4 lead in the third after around more than two hours of play however was left breathing intensely in her seat.
Kasatkina reacted, winning the last three amusements and securing the win on her second match point following two hours 49 minutes.
"Any individual who gets used to misfortunes should abandon life," said Williams, who beat sister Serena in the third round. "I need to quit making that numerous blunders against her."
Osaka, then, has taken her offer of huge name scalps in California, thumping out Maria Sharapova, Agnieszka Radwanska, Karolina Pliskova and now Halep.
That amazing win over the Romanian was her fourth profession triumph over a best 10 player and her second this week subsequent to beating world number five Pliskova in the last eight.
"I feel like there is another age and we are attempting to push through," said Osaka.
Halep had won 18 of her 19 coordinates this season yet the 26-year-old's shape crumpled with this semi-last tied at 3-3 in the primary set.
She lost the following nine amusements, with Osaka keeping her poise to spare four break focuses in the last round of the match before securing triumph on her third match point.
"I was somewhat apprehensive on the grounds that it continued backpedalling and forward," she said. "In any case, I'm extremely happy I could complete on my serve as opposed to breaking her."
Halep was just ready to change over one of her seven split focuses and hacked up 27 unforced blunders as she endured only her second thrashing of the year.
"I simply was not prepared," she said. "I missed the ball a considerable measure and I didn't play what I needed to play. I don't discover pardons. She was better."