The world number three saved four set points against the Italian, ranked 37th, in an opening-set tie-break but turned the tide thanks to some trademark aggression and a bit of luck.
He ended up clinching the set in one hour and 13 minutes, and the complexion of the match then changed completely, as Arnaldi collapsed and left Alcaraz to seal the deal with a smash half an hour later.
The Spaniard will face Denis Shapovalov for a place in the final four after the Canadian, ranked 46th, who prevailed over Chile's Alejandro Tabilo 7-5, 3-6, 6-4.
Tokyo marks Alcaraz's third tournament since returning from a wrist injury that kept him out of action for several months until late August.
He made his comeback at the US Open, losing in the quarter-finals.