With the win, Tsitsipas improved to 11-1 in his ATP Head2Head against de Minaur.
Tsitsipas dominated the match from start to finish, winning in just 69 minutes.
The victory is Tsitsipas's first on clay this season.
Tsitsipas will next face either Jannik Sinner or Hubert Hurkacz in the third round.
"I tried to do the best that I could out there on the court by bringing the best quality on my strokes, and I delivered," Tsitsipas said post-match. "Throughout the entire match I was pretty consistent with my serves and the ball placement. I was able to construct those points patiently and then wait for those shorter balls to come up.
"I really felt that my opponent felt the heaviness and the depth of my ball. It gave me courage, it gave me great belief in myself that I can continue pushing in that sense. I knew that I had something good working for me today."
Stefanos Tsitsipas showcased his exceptional return game and break point conversion skills in his commanding victory over Alex de Minaur at the Internazionali BNL d'Italia on Tuesday.
Tsitsipas won an impressive 56% of his return points (23/41), constantly putting pressure on de Minaur's serve. He also converted on five of eight break points, demonstrating his ability to capitalize on his opportunities.
Despite surrendering his serve once at 4-1 in the second set, Tsitsipas broke back immediately, extinguishing any hope of a de Minaur comeback.
Tsitsipas's impressive performance on clay continues, as he has now reached 12 quarter-finals at the ATP Masters 1000 level on the surface. This ties him for sixth-most all-time, alongside Andy Murray, Carlos Moya, and Albert Costa. Notably, five of these quarter-finals have come in Rome, where Tsitsipas has a strong track record, reaching the final in 2022 and the semi-finals in 2023. He also reached the semi-finals at the event in 2019, one year after qualifying for his tournament debut.
