It appeared Korda had blown his chance to beat the Spaniard on Sunday when he failed to serve out the match in the second set, but he maintained composure, breaking for 4-3 in the third and claiming the victory with an unreturnable serve on match point.
The 32nd seed will next play another Spaniard in the round of 16 after world No.151 Martin Landaluce surprised 15th-seeded Russian Karen Khachanov 6-3 7-6 (7-2).
"I think Sebi was incredible today," said Alcaraz.
"Played such a great game. A lot of tight, tight moments that I just didn't make the most of.
"I think he was better ... so just congrats to him. I think he deserves it."
Korda smacked one of his 12 aces to capture the first set and was on the doorstep of victory when serving for the match in the second with a 5-3 lead, but was broken at love.
The momentum appeared to swing decidedly in Alcaraz's favour from there and he levelled at a set apiece.
But the 25-year-old from Florida refused to back down, going up a break in the decider when Alcaraz's forehand went wide and sealed the win on his second match point opportunity for a first win ever over a top-ranked player.
"It feels great. I took the scenic route, that's for sure," world No.36 Korda said during his on-court interview.
"It was a little more stress than I would want but I'm happy with how I played, happy with how I stayed with it. I got myself into some nasty situations and I kept going, kept believing and I played really well at the end."
Alcaraz, who won the Miami Open in 2022 when he was 18 years old, began the year by winning his seventh major title and completing the career Grand Slam with a triumph at the Australian Open. He did not suffer his first loss of the season until he fell to Daniil Medvedev in the semi-finals at Indian Wells and is now 17-2 on the year.
As he did in 2025, Alcaraz will now have extra time to prepare for the claycourt season, which begins with next month's Monte Carlo Masters.
So too will a demoralised Stefanos Tsitsipas.
After beating Australian No.1 Alex de Minaur in straight sets in round two, the Greek was thrashed 6-0 6-1 by Frenchman Arthur Fils.
In other results, Americans Taylor Fritz and Tommy Paul joined Korda in the fourth round. The sixth-seeded Fritz beat Reilly Opelka 6-3 6-4 and No.22 seed Paul eliminated Raphael Collignon 6-2 3-6 7-6 (7-5).
With AAP & AP.
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