Korda failed to build on an early break as Alcaraz took the opener on Court Philippe-Chatrier, but he appeared to have the Spaniard on the ropes when he forced a second-set tie-break.
However, the two-time grand slam champion clinched the tie-break with a huge forehand winner and seemed to grow in stature from there, moving well and displaying too much power for his American opponent.
Alcaraz put Korda under pressure from the off in the third set and did not give up a single break point on his own serve, converting the first of two match points with a neat serve and volley.
He will face either Ben Shelton or Felix Auger-Aliassime next, with Stefanos Tsitsipas potentially lurking in the quarter-finals.
Data Debrief: Alcaraz just too good
As was the case against Jesper de Jong in round two, Alcaraz looked to be under serious pressure on Friday, only to step things up and pull away from his opponent.
He has now won 14 of his 17 singles matches at the French Open, with his win ratio of 82.4 per cent the third highest among active male players, after Rafael Nadal (96.6 per cent) and Novak Djokovic (85.3 per cent).
The 20-year-old from Atlanta fired down two 149mph serves in one game on his way to a 6-4 6-3 4-6 6-4 victory at Flushing Meadows.
“I think it was straight adrenaline,” he said. “In any other atmosphere I don’t think I could get it done. I think my arm would fall off, but it’s feeling good right now.”
The record fastest serve at the US Open is still held by Andy Roddick, who hit a 152mph thunderbolt on his way to the title in 2003 – the last time an American man won their home slam.
It was sweet revenge for Shelton, who was knocked out by Paul at the same stage of the Australian Open in January.
He added: “I really learned how to be mentally tough. When I was playing in Australia after a long week, I was looking at my box saying ‘my legs are dead, I’m tired, I can’t go anymore’.
“I realised how important it is to believe in myself, believe that I can go all the way, the full distance emotionally and physically and now I have that belief here.”
The Spaniard will face Hubert Hurkacz in the round of 16 of the National Bank Open in Toronto after defeating the fiery American in a competitive affair.
After an even start, a break of serve in the fourth game gave Alcaraz enough of a gap to wrap up the first set in 42 minutes.
The second set was even more competitive, with neither man able to break his opponent until the world number one sealed the victory in a tiebreak.
Meanwhile, American qualifier Marcos Giron upset fifth seed Holger Rune 6-2 4-6 6-3 to set up a third-round clash with compatriot Tommy Paul.
Earlier, veteran Gael Monfils stunned Stefanos Tsitsipas 6-4 6-3, while home favourite Milos Raonic continued his resurgence by seeing off qualifier Taro Daniel 6-4 6-3.
American Mackenzie McDonald knocked out sixth seed Andrey Rublev 6-4 6-3, and second seed Daniil Medvedev is safely through after a 6-2 7-5 win over Matteo Arnaldi.
Thiem won his sole major at Flushing Meadows in 2020, coming from two sets down to beat Alexander Zverev with no crowd present due to the Covid-19 pandemic.
In what turned out to be his final appearance at a grand slam, Shelton cruised to a 6-4 6-2 6-2 victory, before the American led the crowd in a standing ovation for Thiem.
The Austrian has struggled with a wrist injury in recent years, and announced in May that he would be retiring at the end of the 2024 tour.
Thiem was the first Austrian player in the Open Era to receive a wildcard for the men's singles at the US Open, and the first to receive wildcards to multiple grand slam events after last year’s Australian Open
"It's actually a really important moment for me because I had my greatest success of my career here on this court, in a weird 2020 in very strange and different circumstances," Thiem told the crowd.
"I'm super happy that I got the chance to play my last US Open and I can spend some time with you guys, just to say thank you and to make the time up from what we missed four years ago."
Elsewhere, fourth seed Zverev, Andrey Rublev and 2022 finalist Casper Ruud were among the winners in the first round in New York.
The world number one produced arguably his best performance at the grass-court major this year, cruising to a 6-2 6-4 7-6 (11-9) victory on a jam-packed No.1 Court.
Sinner did not have to wait long for his first break against America's Shelton, winning on his opponent's serve to go 3-2 up and then repeating the trick to snatch a 5-2 lead before sealing the first set.
The 22-year-old needed just 29 minutes for that opening-set triumph against the 14th seed, who again struggled to hold his serve in the next set as Sinner reeled off seven games without response.
Shelton eventually ended that imperious Sinner streak by triumphing on his own serve, though the Italian remained perfect with the ball in hand to move within one set of victory.
Sinner lost the first three games of the third set, however, after an early Shelton break, only for the top seed to battle back in his usual fighting fashion.
Having squandered a set-point opportunity, Shelton collapsed to tee up a chaotic tie-break, where both players relinquished multiple chances during an eye-catching duel.
Shelton failed to take any of his three set-point chances, with Sinner also not grasping a match-point opening, though the latter eventually triumphed at the second time of asking.
Sinner's reward will be a last-eight meeting with either Grigor Dimitrov or world number five Daniil Medvedev.
Data Debrief: Super Sinner flying
Since 2000, Sinner is only the fourth player to win 42 or more of their opening 45 ATP matches of a season, along with Roger Federer (2005-06), Novak Djokovic (2011, 2015-16) and Rafael Nadal (2013, 2018).
He is also the fifth male aged under 23 in the past four decades to reach three consecutive quarter-finals at Wimbledon, along with Boris Becker (1988-90), Pete Sampras (1992-94), Andy Roddick (2003-05) and Nadal (2006-08).
The world number one is yet to lose any of his three round-of-16 clashes in SW19, reaching the last eight in 2022, the semi-finals a year later and recording this triumph on Sunday.
