Having celebrated a Triple Crown triumph at Twickenham a fortnight ago, Wales were made to work hard against a side who came close to shocking England in Round 2 and were more than competitive during the first 40 minutes in Dublin last time out.
Wales led by just six-points at the break thanks to a hat-trick of penalties from Leigh Halfpenny compared to one from Mirco Bergamasco but there were plenty of positives to take from a display that had seen them dominate both territory and possession.
Roberts raced clear for a break-away try 10 minutes after the interval to put Wales in a commanding position as he bounced back from the knee problem that saw him replaced against England.
The Blues centre sliced through from fully 50 metres after Wales had won turnover ball on their own 22 to finally give the hosts the size of lead they deserved.
Halfpenny added the extras to move Wales 16-3 in front with half an hour remaining but Italy continued to battle hard, with their life becoming a little easier when the Wales full back was yellow carded less than two minutes later for clashing with Sergio Parisse when both men jumped for a high ball.
Substitutions from both sides saw the game break up in the final quarter but Wales were always the more likely scorers, even when they were a man short.
Rhys Priestland stretched the lead further on 71 minutes while regular kicker Halfpenny was in the sin bin, before Cuthbert rounded off the victory with two minutes to spare.
Captain Gethin Jenkins took a quick-tap to release his club colleague, with the former Sevens star picking off prop forward Fabio Staibano in midfield before racing 45 metres to squeeze in at the corner.
Priestland missed the conversion attempt from the right touchline but it made little difference to the end result.