Having staged a remarkable second-half comeback in France last time out, Warren Gatland's side was far from its best again in Rome against a side whose opening loss at Scotland was a record 18th in succession in this competition.
The boot of Dan Biggar earned the visitors a seemingly commanding 12-0 lead in the first half but Braam Steyn's score and Tommaso Allan's penalty saw that advantage cut to only two.
It was Josh Adams who made a breakthrough 15 minutes into the second period, going over in the left corner at the end of a sweeping move and Owen Watkin made the game safe as Wales moved top of the early table despite Edoardo Padovani's late consolation score.
Wales had trailed 16-0 in Paris last week but needed little more than a minute to forge ahead in Italy as Biggar slotted a simple penalty and added three more before the half-hour as the Azzurri repeatedly transgressed.
Italy belatedly got a foothold in the game and turned down a penalty within kicking range, a decision that was vindicated as it retained the ball from the lineout and worked it right for Steyn to barge over.
Allan struck the post with a chance to reduce the deficit to two at the break but he made no mistake from right in front shortly after the interval.
But Wales finally found some attacking fluency, capitalising on Aled Davies's break and working it left through the hands of Jonathan Davies and Liam Williams for Adams to score.
Davies saw a try ruled out for a knock-on but the game was effectively put to bed 10 minutes from time as Watkin gathered Gareth Anscombe's dink over the top to dot down, rendering Padovani's fine late score academic.
Gatland, who made 10 changes from the France game, will perhaps not be too dissatisfied to see his side head back to Cardiff with two wins in the bag having played well below its usual level.
After back-to-back games on the road to start this year's Six Nations, Wales returns home to face England on 24 February (AEDT) while Italy hosts defending Grand Slam champion Ireland the next day.