Spanish top seed Alcaraz registered a 6-3 6-3 6-4 win over the Italian world number 61.
Wimbledon champion Alcaraz will next face either sixth seed Jannik Sinner or Alexander Zverev, seeded 12th, who play each other later on Monday.
Earlier, Britain’s Jack Draper was beaten by Russian Andrey Rublev.
Rublev will next play either fellow Russian Daniil Medvedev or Alex de Minaur of Australia, with the pair playing in the night session at Flushing Meadows.
Alcaraz was formidable on Louis Armstrong, hitting 31 winners as he booked his spot in the quarter-finals with a one hour and 59 minute win.
The 20-year-old, who beat British number two Dan Evans in the third round, broke midway through the first set and served out the opener to love.
Arnaldi, 22 and playing in his first Grand Slam fourth round, was then broken in the first game of the second set as Alcaraz continued to dominate.
The US Open debutant has had a dream run this fortnight, beating British number one Cameron Norrie last time out, but a shock against two-time major winner Alcaraz always looked a step too far.
The world number 61 did get a break of his own to take a 2-1 lead in the third set but was immediately broken back and, trailing 5-4, was unable to hold serve to stay in the match.
Alcaraz has now won 15 of his past 16 matches at the US Open and is a strong favourite to defend his title.
“When I won Wimbledon I said I’d fallen in love with the grass,” he said after his victory over Arnaldi.
“I’m really comfortable with the three surfaces but right now the hard court is my favourite one.”
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