The world number 111 showed no signs of nerves in his first singles final appearance as he raced to a 6-2 6-1 victory at the ATP 250 clay-court event in Bastad.
After rain delayed the start of the final by over four hours, it took the Uruguayan less than an hour to complete victory - with Sousa only holding serve twice in the match.
When the action finally did begin, Cuevas stormed into a 3-1 lead and he maintained his momentum as the fifth seed floundered, especially on his own serve.
Having managed to get 60 per cent of his first serves in during the opening set, Sousa dropped to only 33 per cent in the second - with Cuevas taking full advantage.
Cuevas won seven successive games to lead 5-0 in the second.
The South American was in complete control in the damp conditions and it was fitting that he wrapped up victory with another unforced error from Sousa to hand him the title.