The Welsh region brushed aside Mogliano 33-0 away last weekend to record their first win in this season's competition and it was an even more emphatic triumph at a rain-swept Rodney Parade.
The Dragons picked up eight tries in total, with scores from Dan Evans, Michael Poole, Wayne Evans and a penalty try helping to put the hosts 29-3 ahead at half-time, before Patrick Leach, Jonathan Evans, Phil Price and Jack Dixon crossed in the second period.
Fly-half Dan Evans added three conversions and a penalty for a personal haul of 14 points, while his replacement Lewis Robling added two conversions in the second half.
The bonus-point victory sees Newport climb above Bayonne, although both teams are level on 11 points, five behind leaders Wasps.
Mogliano, whose only contribution to the scoreboard came from Enrico Endrizzi's ninth-minute penalty when they were 7-0 down, are still without a point as they continue to prop up the group.