Alcaraz was bidding to become the third man in history after Rod Laver and Rafael Nadal to win the French Open, Wimbledon and the US Open in the same calendar year in the Open era.
But the Spaniard never recovered from a shaky start against world number 74 Van de Zandschulp, who triumphed 6-1 7-5 6-4 for the highest-ranked win of his career.
The defeat ends Alcaraz’s 15-match winning run at Grand Slams.
“I think my level stayed at the same point all the match, and it wasn’t enough to win the match or to give myself the chance to get into the match or try to give myself chances,” said Alcaraz.
“I didn’t feel well hitting the ball. I think I made a lot of mistakes. When I wanted to come back or I think I wanted to come back, it was too late.”
The 21-year-old made 27 unforced errors throughout the match while Van de Zandchulp made 21.
“He didn’t make a lot of mistakes that I thought he was going to do so I was confused a little bit,” Alcaraz said. “I didn’t know how to manage that.”
Alcaraz, who won silver at the Paris Olympics after losing to Novak Djokovic on 4 August, says he needed a longer break before going to Flushing Meadows.
“I came here with not as much energy as I thought that I was going to come with. But I don’t want to put that as an excuse,” he said.
Earlier, world number one Jannik Sinner outclassed American Alex Michelsen 6-4 6-0 6-2 for his 50th victory of the year.
Australian Open champion Sinner is playing at his first tournament since it emerged he had been cleared of any wrongdoing after twice testing positive for a banned substance earlier this year.
The crowd on Arthur Ashe Stadium were reduced to silent disbelief when Van de Zandschulp dropped just one game en route to winning the first set.
A below-par Alcaraz seemed to have found his rhythm after breaking back early in the second set, but he lost serve again at 5-5 before his Dutch opponent doubled his advantage.
The three-time major winner looked perplexed as he headed off court for a time-out, wagging a finger towards his player’s box and shaking his head.
Alcaraz found his smile again when he broke back to level the third set at 3-3, but Van de Zandschulp continued to unleash superb winners and clinched the crucial break at 5-4 before serving out the victory with a clinical love hold.
“I am a little bit lost for words, it’s been an incredible evening for me,” said Van de Zandschulp, who reached the quarter-finals in New York in 2021.
“I think from point one here today I believed [I had] a chance.”
The 28-year-old will play British number one Jack Draper in the third round.