Italy continued to disturb Wales but man-of-the-match Alex Cuthbert scorched clear at the death to put the result beyond doubt.
The Dragons can now look forward to a grand slam showdown with World Cup heartbreakers France in a week's time.
Wales were without Sam Warburton, after their inspirational skipper failed to recover from the Championship-threatening knee injury he suffered against England, with Ospreys youngster Justin Tipuric starting in his place.
But they welcomed back former captain Matthew Rees, who reformed the Dragons' all-Lions front-row for the first time since November 2010.
Luke Charteris also made his long-awaited international comeback off the replacement bench following the wrist injury he suffered at the World Cup.
Jamie Roberts came closest to breaking the deadlock after latching on to a Faletau offload. But the burly centre was hauled down short by Luke McLean and Alberto Scarbi.
Wales settled for Halfpenny's third penalty after Bergamasco was harshly penalised at the breakdown. Italy responded with a late rally but Wales held strong to enter the interval leading 9-3.
Wales were frustrated by Italy following the restart of play but Roberts struck with a long-range effort to settle the hosts' nerves.
Alun Wyn Jones pounced on loose ball inside the Welsh half and the ball was spread through Mike Phillips, Halfpenny and Priestland's hands for Roberts to slice through the Azzurri defence.
Halfpenny slotted the extras to hand Wales a 16-3 lead. They continued to cause Italy problems in attack but were dealt a major blow when the full-back was cruelly shown yellow after colliding with Parisse - despite competing for the ball.
Mass substitutions disrupted the flow of the game in the final quarter but Wales hung-on despite their numerical disadvantage.
With Halfpenny in the bin, Priestland stretched the lead further on 69 minutes and Cuthbert rounded off the victory with minutes to spare.
Captain Jenkins took a quick-tap and released Cuthbert, who went outside Fabio Staibano and raced clear before squeezing into the corner.