Now ranked a career-high 19th in the world, the promising 20-year-old would have fancied her chances of pulling off an upset against a player 17 years her senior.
Kasatkina will play another 20-year-old, Naomi Osaka who dismantled No. 1 player Simona Halep 6-3, 6-0.
"I'm a bit exhausted", she said after the 2hr 50min encounter.
Kasatkina's lone WTA singles title came in Charleston, South Carolina previous year.
She was only the fourth unseeded player to reach the Indian Wells final, with the most recent before her being Kim Clijsters in 2005.
She also broke Kasatkina to go up 4-1 with another precision forehand victor down the line and never looked back.
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Neither Kasatkina nor Osaka have much experience in big matches with the Japanese player's only career final coming in Tokyo in 2016 and her opponent's lone singles title coming in Charleston a year ago.
Despite the windy conditions, Williams improved to 5-2 on the season, which includes a third round win on Monday over sister Serena, who was making her return to the WTA after having a baby.
"In one moment you just catch yourself, like, you're in night session, all crowd, you're playing against a legend, and you are in the third set", Kasatkina said. These were certainly the qualities that she displayed throughout her semi-final match against Venus Williams, but it looked as though that might have just left her undercooked in the final. Kasatkina is 1-2 in final appearances for her career and is 0-2 in final appearances on hard court. Philippe Dehaes told her, "She's 37, you're 20".
Kasatkina was surprisingly putting in a lackluster performance and she was slow in her movement, with Osaka exploiting that aspect with her powerful play. With Osaka serving for the match, and the biggest win over her career. She then broke Kasatkina to make it 5-3 and finished it off with another strong service game.
Besides Stephens and Australian Open victor Wozniacki, Kasatkina has beaten the other current Grand Slam titleholders in the past year: French Open victor Jelena Ostapenko and Wimbledon champion Garbine Muguruza. The fact she didn't go to a three-setter until the semifinals should benefit her Sunday.
But she said she never had felt more nervous.
She also alluded to her age, which gave her the willpower to take Williams the distance and breaking her serve seven times in total.