Tsitsipas keeps alive his bid to win his first Grand Slam title, but the 2021 Roland Garros finalist was put to the test early on by Arnaldi who had ousted sixth seed Andrey Rublev in the previous round.
"It was one of the craziest comebacks I've had, the momentum seemed to be going his way the entire match," Tsitsipas said.
"It was very frustrating on my end, because I felt like I was trying my best, trying to make him move, nothing really seemed like it was working."
Arnaldi began strongly, despite needing to save three break points in the opening game. He made the decisive break to lead 3-1 and comfortably saw out the first set, as Tsitsipas was unable to handle the Italian's energy.
Tsitsipas looked in even more trouble in the second set when the Italian broke to lead 3-2, but Arnaldi then failed to take advantage when serving for the set at 5-4 up. Tsitsipas broke and came out on top in the tiebreak to level the match.
"I think experience was the reason I managed to come back today, even at 5-3 in the second set I felt like I can come back," Tsitsipas said.
"I felt like there was power within me to turn this match around and I think that game at 5-4 when I broke him was the biggest pleasure I've experienced in tennis in a long time because I felt there is a chance."
The Greek took his renewed confidence into the third set and broke in the first game. Arnaldi began to struggle and Tsitsipas broke once more, and two further breaks in the fourth set put an end to the Italian's challenge.
"He's one of the biggest fighters I have played in tennis and he deserves a lot of credit because he was pushing me to the limits and one of the strongest opponents I have had on the clay court season so far," the relieved winner said.
"I really think we are going to see a lot of things from him in the future because there are players at certain moments that are a little more fragile but he seemed very composed and very strong in those crucial moments."
Tsitsipas will face Spanish third seed Carlos Alcaraz next, a repeat of last year's quarter-final which the Greek lost.
Alcaraz has won all five of their previous meetings.
"He said in the past that he likes playing against me, so I hope he gets to like it a little bit less the next time," Tsitsipas said with a smile.
