The 19-year-old dragged his weary body to a 6-4, 2-6, 7-6 (7/1), 6-3 victory over Norway's Casper Ruud in the final.
Alcaraz, the first teenager to claim the top ranking, is the youngest Grand Slam men's champion since Rafael Nadal at the 2005 French Open after a performance which yielded 55 winners and 14 aces.
On a day of landmarks, he is also the youngest champion in New York since Pete Sampras in 1990.
It was a gruelling tournament for Alcaraz who claimed the record for most time spent on court at a single Grand Slam event, passing the 23 hours and 21 minutes it took Kevin Anderson to finish runner-up at Wimbledon in 2018.
Defeat for Ruud, who was also vying for the world number one ranking, was his second in a Slam final this year after he was routed by Nadal in the French Open.
With the roof closed, the Arthur Ashe Stadium crowd observed a moving moment's silence on the 21st anniversary of the September 11 attacks before the final got off to a tentative start.
Both men saved break points in their opening service games before Alcaraz gained the only break of the first set for a key 3-1 lead.
Ruud dropped the set but triumphed in terms of sportsmanship when he called a double bounce on himself in the eighth game, conceding the point to the Spaniard.
Alcaraz served it out to love and a one set lead courtesy of his 13 winners to six for the Norwegian.
The Spanish teenager, who went into the final with a 2-0 winning record over Ruud, squandered a break point at 2-2 in the second set.
Ruud made him pay, edging ahead for 4-2 and then levelling the final on a second set point after another careless Alcaraz drop-shot opened the court invitingly for the Norwegian.
At that moment, Alcaraz had been on court at the tournament for almost 22 hours, passing the mark set by Andy Murray when the Briton claimed the 2012 title.
He was ahead for 2-0 in the third set before Ruud hit back.
The 23-year-old Norwegian had two set points in an 11-minute 12th game but was unable to convert as Alcaraz put away inch-perfect, back-to-back volleys.
Alcaraz made the most of his reprieve, racing through to his first tiebreak success of the tournament as Ruud's game fell suddenly apart.
The Spaniard sensed his chance, breaking for 4-2 in the fourth set before taking his aces count to 12 to lead 5-2.
Ruud held to love but Alcaraz claimed his slice of history on a second match point before collapsing to the court in celebration.
Highlights US open Carlos Alcaraz Casper Ruud