Some dazzling shot-making from the world number one had the crowd on its feet but behind the fun-filled evening were some flaws as Alcaraz piled up 29 unforced errors and showed a lack of concentration at key moments.
Even while not at his best though, he could rely on raw talent and a vast repertoire of shots to see off the 177th ranked South African. But the 20-year-old will need to improve with rival Novak Djokovic on the prowl for a 24th Grand Slam and seeking revenge for his Wimbledon loss to the Spaniard.
"I think I played great, a great match," assessed the Spaniard. "But obviously in the third set he started to play better. I got down a little bit.
"In the end, I think I played a pretty good match and will try to keep the same level."
There was little to learn from Alcaraz's opening match on Tuesday against Dominic Koepfer, which was cut short when the German retired with an ankle injury.
Harris is recovering from wrist surgery and has seen his ranking drop but the big-hitting South African is a proven danger man, reaching the quarter-finals in 2021 and having a few top 10 wins on his resume, including one over Rafa Nadal.
The contest got off to a cautious start before Alcaraz began to settle into the match, taking control of the first set with a break to go up 3-2. From that point on he dialled up the pressure and clinched the set with a second break.
Alcaraz continued to dominate in the second but lost focus in the third, committing 16 of his 29 unforced errors, as Harris threatened to take the contest to a fourth set before losing the tie-break 7-4.
There will be no room for such lapses in the third round for Alcaraz with 26th seed Dan Evans waiting in the wings.
"It's a really tough player, good serve and volley, good net game," said Alcaraz. "It's going to be really tough.
"I will have to return very, very well if I want to win that match."
Daniil Medvedev meanwhile survived a late-night scare by taming Australian battler Christopher O'Connell 6-2 6-2 6-7(6) 6-2 to reach the third round at Flushing Meadows.
After strolling to a two-set lead he had looked headed for routine passage but in the end, the third-seeded Russian needed all his resolve to push O'Connell to the exit.
The party atmosphere inside Louis Armstrong Stadium was starkly different from the last time Medvedev and O'Connell stood across from each other during the dark days of COVID-19 restrictions.
That 2020 second-round match, which O'Connell described as "eerie", was played in an empty arena with the exception of the players, their coaches and officials while Thursday's clash was electric, with roars erupting after almost every point.
Medvedev broke to open both the first and second sets and was in complete control until O'Connell tapped into the energy of the crowd that was now squarely in the Australian's corner.
With chants of, "Aussie, Aussie, Aussie, Oi, Oi, Oi" rising from the stands, O'Connell dug in to take the third set to a tiebreak when a shaky Medvedev double-faulted to hand him a well-deserved third set.
But Medvedev did not become the 2021 US Open champion without surviving a few tests and used that experience to regroup, breaking O'Connell to go up 3-1 in the fourth and never letting the Australian back into the set.
On the women's side, Jessica Pegula crushed Patricia Maria Tig 6-3 6-1 to set up an enticing third-round clash with Elina Svitolina.
The clean ball-striking of the top-ranked American was more than the world number 700 from Romania could handle in a match that lasted just over an hour.
Pegula, seeded third, never trailed in a contest where she won 80% of her first serve points and broke Tig's serve six times.
Next up for the Buffalo native is Ukrainian Svitolina, who came from behind to beat Anastasia Pavlyuchenkova of Russia earlier in the day.
Pegula edged Svitolina in a three-set battle in Washington D.C. earlier this month and holds a 3-1 advantage in their career meetings.
"Every single match we play is just a really good battle," Pegula said.
"I feel like we play to each other's games where we make each other play better and we always have really great matches."
"It's great to see her back, playing at such a high level so quickly. I just played her a few weeks ago so it's going to be very tough," she said.
Elsewhere, Russian Daria Kasatkina battled back to defeat American Sofia Kenin 2-6 6-4 6-4 and reach the third round, while last year's runner-up Ons Jabeur was made to work hard by Czech teenager Linda Noskova before sealing a thrilling 7-6(7) 4-6 6-3 victory.
The Tunisian fifth seed, who is seeking a maiden Grand Slam title, edged a tight opening set before 18-year-old Noskova stepped up the pressure in the second.
Noskova had won their only previous meeting in the Adelaide semi-finals earlier this year and breezed to a 5-1 lead before Jabeur came storming back by winning three quick games.
Jabeur, who was dogged by breathing difficulties and other issues in her last match, took a tumble chasing a low shot at the net and appeared shaken up briefly as the big-hitting Noskova held her serve to level the match.
The Tunisian said she was still not at 100% but added that playing in the night session had helped her.
"But yeah, I'm taking it slow," Jabeur said. "Not really slow in this match, but I have one day off and hopefully I'll feel better after tomorrow.
"It's tricky to feel sick during a tournament so we manage with the team. Let's see what's going to happen."
Jabeur saved a break point to go 2-1 up and eventually took charge of a tense decider in the eighth game before closing out the win on her fourth match point, setting up a meeting with another Czech, Marie Bouzkova.
