Korda notched his first victory over a world number one, sending Alcaraz to his second straight early exit in Miami -- where Alcaraz lifted the trophy in 2022 but lost his second-round opener to 55th-ranked Belgian David Goffin last year.
It looked like Korda had missed his chance when he served for the match at 5-4 in the second set and was broken at love.
Alcaraz won the next two games to force a third set. The Spaniard stepped up his intensity, but Korda didn't buckle and it was Korda who seized a break for 4-3 in the third when Alcaraz sailed a forehand wide.
He held his next service game with confidence, slamming down an overhead winner on game point and after Alcaraz held serve to force Korda to serve for the match again, the American made no mistake, sealing victory on his second match point as Alcaraz sent a service return long.
"It feels great," said Korda, who has been ranked as high as 15th in the world but has endured two seasons disrupted by injury.
"I took the scenic route, that's for sure - a little more stress than I would want but happy with how I played, happy with how I stayed with it.
"He's unbelievable in every aspect of his game, movement, volleys, forehand, backhand, there's nothing he can't do," Korda said of Alcaraz, who won the Australian Open in January to become the youngest man to complete the career Grand Slam.
The 22-year-old Spaniard had followed that up with a title in Doha and had pushed his unbeaten 2026 record to 16-0 before falling in the semi-finals at Indian Wells this month.
Korda will face either Spanish qualifier Martin Landaluce or 14th-seeded Karen Khachanov for a place in the quarter-finals.
Sabalenka, Zheng move on
World number one Aryna Sabalenka kept her title defense on track with a 6-4, 6-2 victory over 72nd-ranked American Caty McNally that was tougher than the score indicated.
They were on serve after exchanging four breaks in the opening set when Sabalenka gained the decisive break in the final game.
The Belarusian star, trying to complete the "Sunshine Double" after capturing her first Indian Wells title last week, wasted one chance to break in the second set before ramping up her return pressure to break McNally's on her last two service games.
"She played really great tennis," Sabalenka said, adding that her hold for 5-4 in the opening set, in a game that went to deuce five times, was key.
"(I'm) super happy to close this match in straight sets," said Sabalenka, who booked a meeting with China's Olympic gold medallist Zheng Qinwen, a 6-2, 6-4 winner over Madison Keys.
It was Zheng's first win over a top-20 player since elbow surgery last July.
World number two Elena Rybakina, who beat Sabalenka in the Australian Open final but fell to her in the Indian Wells title match, moved smoothly into the last 16 with a 6-3, 6-4 victory over Ukraine's Marta Kostyuk.
Rybakina next faces Australian qualifier Talia Gibson, who knocked off another seed with a 6-2, 6-2 victory over 18-year-old 18th seed Iva Jovic.
Gibson, who reached the quarter-finals at Indian Wells, had ousted former world number one Naomi Osaka in the second round.