Jonathan Davies and Alex Cuthbert scored the crucial tries while Leigh Halfpenny booted 16-points in a second consecutive man-of-the-match performance.
But it was the dominant forward eight that laid the foundations with an impressive scrummaging display.
"Our scrum was outstanding," said Roberts.
"Adam (Jones) was magnificent, as were Gethin (Jenkins) and 'Hibbs' (Richard Hibbard). I take my hat off to the forwards - they worked so hard.
"Tight games are often decided by things like a bounce of the ball, but we got our just reward.
"Defensively we were strong as well. The communication was good. We've been doing a lot of hard work with Shaun
Edwards, and not to concede a try away to Italy is an achievement."
Wales face Scotland at Murrayfield next and a victory would set up a potential title decider with England.
And Roberts was thrilled with the manner in which Wales ground out a win in difficult conditions.
"It was a very pleasing win," added Roberts.
"We wanted to play rugby, but we had to adapt our game because of the weather.
"We had to play 10-man rugby with the backs chasing the ball, but it was great to win and it sets us up to face a much-improved Scotland side at Murrayfield in a couple of weeks.
"We would like to have played an expansive game, but we couldn't in those conditions, and I thought we adapted our game well and fronted-up well.
"The game seemed to hinge on Jonathan Davies' try. It swung things in our favour and it really did prove to be pivotal."