Tom Prydie scored a try and kicked the rest of the Dragons' points at Stadio Comunale di Monigo but the visitors had no answer to the greater attacking threat of the Italians, who ran in tries by Edoardo Gori, Christian Loamanu (2), Luke McLean and Tobias Botes.
The Dragons went ahead in the second minute as Prydie kicked his first penalty of the day, but Gori crossed for Treviso's opening try seven minutes later, with Alberto Di Bernardo adding the extras.
Di Bernardo's penalty further extended the home side's lead before Prydie reduced the deficit.
Loamanu crossed on 25 minutes to restore Treviso's cushion, while McLean added a third try before the break. Di Bernardo missed both conversions to restrict the hosts to a 20-6 half-time advantage.
Loamanu added his second try two minutes after the restart before Prydie crossed for the Dragons' sole try of the afternoon on 52 minutes.
Will Harries saw red after 61 minutes as the Dragons' discipline started to waver, and Treviso sealed the victory in the 72nd minute as Botes went over.
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