Both sides scored two tries apiece but the boot of Stephen Jones who claimed 11 points proved the difference after Itlay sharp shooter Mirco Bergamasco had a day he would rather forget when shooting for goal.
Wales coach Warren Gatland was in a satisfied mood after the game, saying: “This is a tough place to come to and get a result. We made it difficult for ourselves in that we conceded a couple of soft tries, but we are very pleased with the result.
“We looked really sharp with the ball in hand at times, although we could have expressed ourselves a bit more in the second-half.
“Italy are a big physical side, but they played a lot more rugby today and showed how difficult a team they are to beat in Rome.
“They missed a couple of shots at goal, but credit to our guys. They soaked up a lot of pressure and then went upfield and got three points through the drop-goal.
“Ireland struggled here a few weeks ago, and this game has been a real banana skin for us in the past.”
“Ireland is a big game for us coming up in a couple of weeks, and then it’s France away. This is a tough competition, but it is about building momentum and confidence.”
Skipper Rees, who led front the front with an outstanding performance at hooker, said: “It was a very tough match but our defence was great. It was our defence who kept the Italians out of the game.
“We can definitely win the title. That is two wins on the trot and we have a home game to come against Ireland and then round it off with a huge match against France in Paris.”
