Torrential rain made life tough for the reigning Six Nations champions, but second-half tries by centre Jonathan Davies and wing Alex Cuthbert gave the Welsh something to sing about.
Full-back Leigh Halfpenny chipped in with 16 points from four penalties and two conversions as Wales recorded a fourth successive Six Nations away win for the first time since the championship began 13 years ago.
It sets them up for appointments with Scotland and England next month knowing a retention of Six Nations silverware won in Grand Slam fashion last season is not beyond them.
"I am very pleased," said Wales' interim head coach. "We adapted really well to the conditions and the deluge. We showed patience and composure and we took our opportunities. Our scrum was very impressive and gave us the platform."
The only sour note for Wales was a calf-muscle injury to prop Gethin Jenkins that could make him a doubt against Scotland on March 9.
For the second successive Six Nations Test, Wales did not concede a try, and Italy rarely threatened as Wales recorded a third successive win in Rome.
"The first half was tough. The conditions had a huge impact on the way both teams played, but our game management was excellent," said skipper Ryan Jones.
"All 23 players showed composure and maturity. It was a good day at the office in the scrum – there are six very happy front-row forwards in our changing room."
Forwards coach Robin McBryde was delighted his pack responded so strongly after a testing time in Paris two weeks ago.
"Fair play to the players. A scrum is a collective effort, and as an eight they stood up and exerted pressure," said McBryde
Italy captain Martin Castrogiovanni had no complaints after seeing his team suffer a second successive comprehensive Six Nations reversal following their 34-10 loss to Scotland a fortnight ago.
The Leicester prop, stand-in skipper for suspended Sergio Parisse, capped a miserable day by being sin-binned midway through the second period, and Wales scored a try in his 10-minute absence.
"We conceded nine points from scrums, which is my problem as well as the team's. I need to work on that," he said. "The referee is always right. If we had done what we were told and managed our kicking game better, maybe the referee wouldn't have mattered so much.
"There are no excuses. You need to be perfect in all aspects, but we weren't today. I was very honoured to be made captain, but I don't like losing. I hate losing even when I am playing PlayStation.
"We didn't really handle some areas very well. There are ups and down in life, and today was one of the downs."
Italy coach Jacques Brunel added: "I don't think the problem was our ability to play, we just didn't manage the game very well. Wales were a lot more precise than us. That was the difference."
Italy: Masi, Venditti, Benvenuti, G Canale, McLean, Burton, Gori, Lo Cicero, Ghiraldini, Castrogiovanni, Pavanello, Minto, Zanni, Favaro, Vosawai.
Replacements: Giazzon (for Ghiraldini, 55), De Marchi (for Lo Cicero, 55), Cittadini (for Vosawei, 65-69), Geldenhuys (for Minto, 55), Derbyshire (for Zanni, 70), (for Gori, 65), Orquera, Garcia (for Canale, 64).
Wales: Halfpenny, Cuthbert, Davies, Roberts, North, Biggar, Phillips, Jenkins, Hibbard, A Jones, Coombs, Evans, R Jones, Tipuric, Faletau.
Replacements: Owens (for Hibbard, 52), James (for Jenkins, 46), Mitchell (for A Jones, 74), Wyn Jones (for Coombs, 52), Warburton (for R Jones, 69), Lloyd Williams (for Phillips, 64), Hook (for Biggar 69), Scott Williams (for Roberts, 70).