The Azzurri ended a 14-match losing streak in the competition with a 30-22 triumph over Steve Hansen's Welsh side at the Stadio Flaminio yesterday.
"This was a very important win for Italian rugby," said Dominguez, whose side's only other victory in the tournament came on their debut against Scotland three years ago.
"We are a big country but a small nation in rugby terms but this victory shows that we have arrived on the scene," he said.
"This is one of the best moments of my career, and it is always nice when you get games like this. I am very happy."
The 73-times capped player converted all three Italian tries - scored by Giampiero De Carli, Carlo Festuccia and Matthew Phillips - and controlled the game with scrum-half partner Alessandro Troncon.