Fullback Halfpenny missed only one kick in the torrential rain in Rome, while centre Jonathan Davies and right wing Alex Cuthbert scored second-half tries.
Italian captain Martin Castrogiovanni, taking over from the suspended Sergio Parisse, was sent to the sin bin in the second half after being shown a yellow card for repeated scrum infringements in the front row.
Wales now have two wins from three matches while Italy, who upset France in the first round, have lost twice.
The Italian scrum, normally one of the team's strengths, failed to contain a committed Welsh eight and they rarely looked like breaching the visitors' defence. Flyhalf Kris Burton kicked all their points with three penalties.
"The first half was tough and the conditions had a huge impact on the way both teams played. The game management was excellent. To come here and beat Italy you need composure," said Wales captain Ryan Jones.
"Our attitude was superb. You can never question our never-say-die attitude. We dug real deep and showed what we're made of as a team."
Coach Rob Howley said the Wales' scrum had given his team the platform for victory.
"In the second half we were clinical and took our opportunities," he said. "We had three opportunities and scored two tries, that's a testament to this side."
ATROCIOUS CONDITIONS
Castrogiovanni said the Italian scrum had been a weak point.
"We conceded nine points from the scrum today and that's also my fault because I was the leader out there today. We'll have to look at the videos but today we just weren't there," he said. "We have to be at our best in every aspect of the game and today we weren't that."
With the score 9-6 to Wales after a uneventful first half, the game turned on two errors early in the second half.
Italy should have scored the game's first try in the first minute of the second period when Tommaso Benvenuti failed to gather Burton's chip over a charging Welsh defence only metres from the try line.
Wales extended their lead to 16-6 four minutes later when another chip, this time from scrumhalf Mike Phillips, bounced awkwardly and Davies capitalised on indecision in the Italian defence to snatch the ball and race through to score unchallenged.
Cuthbert moved Wales further ahead just after the hour mark, finishing a spell of Welsh pressure by racing through the defence at an angle to score in the corner.
Halfpenny, whose kicking was magnificent all day, converted brilliantly to make it 26-9 and secure the two points.
"In the first half we didn't manage territory well, and they did with long kicks and pressure," said coach Jacques Brunel.
"It's true that we were only at 9-6, but we never had control of the game. They controlled the play, especially with the boot and in the scrum.
"They were more precise than us in their play. We didn't manage to put any pressure on them.
"In the second half we had the chance to score and five minutes later they have a similar kick and they score from it. That's the difference."
