Kasatkina, who came within two points of defeat in the final set over Venus Williams on Friday before winning 12 of last 16 points, became even tenser and indulged in an untimely streak of loose errors. Halep is 26 years old. "Of course, we were both nervous at the beginning, because the biggest finals so far".
The top seed battled through three closely matched sets amid windy conditions on court to win 6-4 6-7 (5/7) 6-3.
Halep moves on to the semi-finals where she will face Japan's Naomi Osaka who beat fifth-seeded Karolina Pliskova 6-2, 6-3.
Kasatkina was surprisingly putting in a lackluster performance and she was slow in her movement, with Osaka exploiting that aspect with her powerful play.
The Russian has been toppling big names all tournament long, also defeating US Open champion Sloane Stephens and World No 2 Caroline Wozniacki on the way to the semi-finals.
World No. 1 Simona Halep and former No. 1 Venus Williams were pushed to the side by Russian Daria Kasatkina and Japan's Naomi Osaka in the BNP Paribas Open semifinals to unveil the next generation of stars on Friday at Indian Wells.
Naomi Osaka seeks her first career WTA singles title. Halep blasted two aces and broke Martic's serve four times. Little wonder, perhaps, given the size of the stage and the size of the occasion.
Both born in 1997, both knocking out some huge names en route to the final, Osaka and Kasatkina are enjoying a statement week in the California desert and have one clear message to the world.
But the Japanese gave her a lesson on how to deliver a ideal down the line backhand victor, Kasatkina's best stroke, to break to 5-3.
The young Japanese, who will crack the top-30 for the first time when the new rankings are released on Monday, turned around a 0-3 record against Halep by claiming a first victory over the Romanian. I just knew that she was going to fight for every point, too. So too, however, is Kasatkina. "That's pretty much all - I mean, I have to stop making that many errors against her".
Osaka served a love game to go up 5-1.
Venus Williams won just two more points as Kasatkina took the last two games to close out the match in 2 hours, 48 minutes.
Until Indian Wells, Osaka had made it past the quarterfinals at a WTA event just once, when she was runner-up in Tokyo 18 months ago. She was ready to play and ready to win the match.
"I just didn't feel the ball at all". It seems unlikely: the only sign of her nerves and lack of experience surfaced as she lifted the heavy BNP Paribas Open trophy.
After nervously hesitating in ticking off thank-yous, Osaka said, "This is probably going to be the worst acceptance speech of all time".
It was far from flawless, but charming nevertheless.
But that's more than she cared to consider, especially against Kerber.