The 22-year-old Alcaraz became the youngest man to complete a career Grand Slam with his Australian Open triumph this year. He followed with a title in Qatar and took a 16-0 record into Saturday's semi-final.
But Medvedev was up to the challenge, last month's Dubai champion running Alcaraz ragged as he pushed his own ATP win streak to nine matches with an impressive victory.
Former number one Medvedev's aggressive play from the baseline and superb serving performance had Alcaraz on the back foot throughout, his control in the rallies leaving Alcaraz gasping after one long point in the ninth game of the second set.
Alcaraz went on to hold serve in that game, but Medvedev saved a pair of set points in the next and dominated the tiebreaker to reach the Indian Wells final for a third time.
The 30-year-old lost to Alcaraz in the title match in both 2023 and 2024.
"Super happy to beat someone as strong as he (is)," Medvedev said. "It's a great feeling."
Medvedev needed just one break to pocket the opening set. Alcaraz broke first in the second for a 3-1 lead, but Medvedev immediately broke back and when they came to the tiebreaker was in full control, powering to a 6-1 lead.
"He's an amazing player with amazing shots, defense, attack, serve, return, everything," Medvedev said. "So you need to be at your best - and I was."
Sinner sees of Zverev to make maiden Indian Wells final
World number two Jannik Sinner powered past Alexander Zverev 6-2, 6-4 in Saturday's first semi-final.
Sinner saved the only break point he faced in a commanding display of precision and power.
Zverev delivered two impeccable service games before he began to falter.
Sinner broke him twice as the German's errors began to climb, including forehand miscues on both break points.
Zverev cut a dejected figure after Sinner pocketed the opening set in 31 minutes and was close to falling in an early hole in the second when he fell behind 15-40 in the opening game.
Zverev fended off three break points in the game, finally managing to push Sinner into some extended rallies as he sealed a hold with a pair of massive serves.
Playing with renewed energy, Zverev conjured his first break chance in the sixth game, but Sinner saved it with an ace and promptly broke Zverev in the next game to gain the only advantage he needed.
Sinner, who fell in the Indian Wells semi-finals to eventual champion Alcaraz in 2023 and 2024, has now reached the final of all six hardcourt ATP Masters 1000 events.