De Minaur, who got the better of Novak Djokovic, Alexander Zverev and Taylor Fritz at the United Cup team event, beat Arnaldi 6-3, 6-0, 6-3 to move into the third round for a fourth straight year.
While the Australian number one eventually claimed a comfortable win on Wednesday, he was made to work in the first set by Arnaldi and twice had to save breakpoints to preserve his early lead.
De Minaur also let his concentration slip briefly towards the end of the match and was broken by Arnaldi while leading 3-1 in the third set, though he recovered well to seal the victory.
"I feel in a good position where maybe I know if I don't bring my A game, I've still got plenty to show. I've won enough matches this year to kind of know how to win certain types of matches ...," De Minaur told reporters.
"I think so far I have done what I needed to do to win the matches. It hasn't been probably the prettiest of levels or my best level.
"I played two opponents where maybe I haven't been allowed to be as aggressive as I would like, because, you know, they've got a lot of firepower. But I do think I've got a lot more to show."
De Minaur next faces Italian qualifier Flavio Cobolli.
