Lyn Jones' side scored seven tries in total in a 50-8 success that puts them on the front foot in a group that also includes French Top 14 team Bordeaux-Begles.
Italian outside-half Kris Burton added 15 points with the boot in a fine kicking display that saw him miss just once from the tee.
Centre Ross Wardle crossed for the first try after just seven minutes as he danced his way through from close-range. Burton added the conversion having already struck a fourth-minute penalty and the Dragons were 10 points to the good.
Mogliano full back Nicolo Fadalti missed his first chance to put points on the board from the floor and the Dragons made him pay with a brace of tries in four minutes midway through the half.
Prop Francisco Tetaz Chaparro powered over down the left-hand side after 19 minutes, before scrum-half Jonathan Evans scored with a sniping run moments later. Burton completed both seven-point scores to push the Dragons into a commanding 24-0 lead.
The Italian part-timers did at least get off the mark with a well-struck penalty from Fadalti two minutes before the half hour but the Dragons had the bonus point sewn up shortly afterwards as Will Harries dived over just to the left of the posts for the first of his two tries. Jon Evans' quick tap penalty left the Mogliano defence in no man's land inside their own 22 and Tom Prydie's clever flip pass gifted Harries a simple score.
Burton continued his perfect record from the tee with his easiest attempt of the night and the hosts were 31-3 up and coasting.
The second half started slowly as far as the Dragons were concerned as they failed to add to their tally until Harries claimed his second try just before the hour mark.
Blindside flanker Ieuan Evans quickly added a sixth score, though, with Burton seeing his 100 per cent record go amiss at last.
Mogliano grabbed a consolation score through centre Tommaso Boni after replacement Dragons lock Adam Jones became the third player to be sent to the sin bin following Nic Cudd and Enrico Endrizzi's earlier offences.
But the Dragons had the last word through Adam Hughes with five minutes left and Burton's sixth conversion ensured they finished with 50 points.