Jonathan Davies and Alex Cuthbert scored second-half tries and man of the match Leigh Halfpenny was again on song with the boot as he added 16 points from the tee.
Davies crossed four minutes after the break following a clever box kick from 2009 Lion Mike Phillips, while Cuthbert sealed the win by cutting though on the hour mark.
Wales dominated large chunks of the first period but only led 9-6 at the interval after a hat-trick of Halfpenny penalties were met by a brace from Brisbane-born Italian outside-half Kris Burton.
Scarlets centre Davies swung the game significantly in the visitors' favour when he made the most of a fortunate bounce after both Burton and halfback partner Eduardo Gori had failed to gather Phillips' dink over the top from the base of a ruck.
Halfpenny's extras pushed Wales 10 points clear and they never looked like relinquishing that lead in atrocious conditions in Rome.
Burton continued to favour putting boot to ball rather than keeping it hand despite the deficit and it was the Welsh who were rewarded when they defied the conditions and went wide after wining attacking lineout ball.
Cuthbert picked a superb line on the outside shoulder of Dan Biggar after both Davies and Jamie Roberts had run dummy lines to suck in Gonzalo Canale and co, and the Cardiff Blues wing finished brilliantly on a right to left arc to punish Italian captain Martin Castrogiovanni just moments after the Leicester prop had been sinbinned for a scrum offence.
The touchline conversion that followed from Halfpenny proved to be the final score as the game petered out in the last quarter, with Italy never threatening the Welsh line long enough to raise home hopes.
Wales will now head to Scotland in two weeks' knowing a win at Murrayfield - and a sixth tournament away success in a row - would see them in line to challenge for the title against England in Cardiff on the final Saturday of action.