Thiem, who is second only to Novak Djokovic in match wins for 2016, needed just over an hour to defeat Sousa, who was coming off the back of a quarterfinal run in Madrid, 6-3 6-2.
The 22-year-old Austrian will now face a tantalising encounter with Roger Federer on Thursday for the right to reach the quarterfinals in the Italian capital.
Thiem edges topsy-turvy opener
Thiem elected to serve first in the match, but his tactic appeared to backfire as Sousa came out firing and secured a break in the opening game. However, holding serve was to prove even more difficult for the Portuguese, who proceeded to lose his service in the next three games.
Thiem was hardly comfortable on serve himself, losing two of his first three games, but his superior power and movement meant that he was always in control of the set, taking it 6-3.
Late flurry gives Thiem comfortable victory
Sousa had been on the back foot for the majority of the opening set, but he started the second in aggressive fashion, coming into the net and sealing a comfortable hold. Both men exchanged holds to love before Sousa had two chances to break the Austrian at 2-1. Thiem saved both break points, and in the next game benefitted from a replayed point and a shanked forehand from the Portuguese to secure the opening break of the second.
Thiem was now in full flow, and after securing another hold for 4-2, broke Sousa again with a masterclass of backhand drop shots, showcasing his superior touch. The world number 15 sealed his win with a series of wide serves and big forehands, giving him the opportunity to have a crack at world number two Roger Federer on the dirt.
Making just 51% of his first serves, Thiem's victory wasn't as a result of flawless delivery. He won 69% of points behind his first serve and an impressive 64% behind the second, but it was hardly an exemplary serving performance.
Instead, Thiem's victory was as a result of his ability to attack the Sousa serve, particularly the second. Sousa made an impressive 68% of his first serves but won just 54% of points behind it, and a paltry 31% on his second serve. Thiem's ability to attack Sousa's serve was the key to his comfortable victory, breaking the Portuguese's serve five times from six attempts in just nine service games.