The future is now at the BNP Paribas Open.
"We are coming", Kasatkina said of the next generation of young players.
Federer had a chance to serve out the match, holding two match points.
"I'm a bit exhausted", Kasatkina said during an on-court interview after the match.
It was, for both up-and-comers.
Unable to get her serve on track, Halep was denied the rhythm common in most of her victories.
The final is an appetizing feast of varied styles pitting Kasatkina's varied spins and speeds and court sense against Osaka's prodigious power and shot-making.
'I just fought till the end, and I think that's why I could win.
"I don't care what's happening on court, I just try to execute my game", Williams said.
"I just really tried to be consistent".
Osaka forecasts fun for her first-ever clash vs. Kasatkina, who has won nine of her last 10 matches.
Alyssa Roenigk is a senior writer for ESPN The Magazine and ESPN.com whose assignments have taken her to six continents and caused her to commit countless acts of recklessness.
Kasatkina has defeated four top-20 opponents at the same tournament for the first time in her career.
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Osaka, the world #44, was unseeded and so began in the first round, defeating the four-time Grand Slam champion and former #1 Maria Sharapova to reach the second round.
Kasatkina, who wasn't even born when Williams first competed at Indian Wells, said she really felt the nerves getting to her on the big stage in the final. Halep was swept away, by a wave of powerful ground strokes and heavy serving, in just over 60 minutes, not to mention the number of unforced errors that Halep made.
"So I love it, I'm happy".
"Anyone who gets used to losses should give up on life", Williams said. Osaka is yet to win a WTA singles title. Philippe Dehaes told her, "She's 37, you're 20. Make her work!" demanded the Belgian coach. The Russian tossed up lobs over the 6-foot-1 American - some worked, some didn't, but she remained unflappable.
Indeed on all-access day at this tournament, the same question about the World No. 1 ranking looking set to bounce around for a few months came up repeatedly.
Along with Osaka, Kasatkina too is having an impressive run so far. "She improving so much, so she's really unsafe player".
Prediction: Kasatkina in three sets. The fact she didn't go to a three-setter until the semifinals should benefit her Sunday.
"Sure", she replied, and they slapped hands. And that emboldened Osaka, who pulled of a smash victor and then a big forehand to break in fifth game, and backed it up with a love hold. On the very next point Martic hit a forehand wide as Halep took the game and a 5-3 set lead.
Williams double-faulted twice in a row to drop serve and trail 6-5. It was really tough match, yeah. The players exchanged breaks at the top of the first set but from that point on it was all her.
"We've had a lot of great matches", Williams said of playing Suarez Navarro. Williams won 10-8 in the third set.
No. 19 Kasatkina was just two points from losing the match, trailing 4-5 and 0-30 in the third set.
She also broke Kasatkina to go up 4-1 with another precision forehand victor down the line and never looked back.
He will now face Argentina's sixth seed Juan Martin Del Potro for a place in the final.
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