It took the Dragons just four minutes to get off the mark as hooker Rhys Buckley crashed over from close range following a quick break from fly half Jason Tovey.
The lead was extended just minutes later as centre Adam Hughes touchdown followed by Aled Brew and Andy Tuilagi, the latter collecting the bonus-point score.
On the stroke of halftime Tovey ghosted through the Prato defence and enjoyed an unchallenged canter to the line for his side’s fifth try of the game.
Prato came out fighting in the second half and were rewarded with a Alberto Chiesa try.
The Dragons then hit back with two tries of their own through Martyn Thomas and Lewis Robling to round off the victory whilst Prato claimed a late consolation but the result was never in doubt.