Paul Turner's men followed Leinster and the Scarlets in losing out to the impressive Italians as their poor start to the year continued.
Tries from Scott Morgan and Chris Price saw the Dragons draw level at 13-13 with a quarter of an hour remaining but a late Chris Burton score saw Treviso home 20-13.
Burton crossed with just four minutes remaining as the Dragons were forced to settle for just a losing bonus-point despite having fought back from a 13-3 deficit.
The Dragons now sit just one place off the foot of the table after their fourth defeat of the season.
Next up is a trip to Glasgow in the first round of the Heineken Cup this Friday, followed by a huge encounter with reigning European Champions Toulouse at Rodney Parade eight days later.
Treviso: Botes, Nitoglia, Galon, Vilk, De Jager, Burton, Semenzato, Vosawai, Derbyshire, Barbieri, van Zyl, A. Pavanello, Cittadini, Ghiraldini, Rouyet
Replacements: Benvenuti for Nitoglia (80), Picone for De Jager (62), Williams for Semenzato (47), Zanni for Vosawai (24), E. Pavanello for van Zyl (62), Sbaraglini for Cittadini (47), Di Santo for Rouyet (47)
Dragons: Harries, Hughes, Cheeseman, Riley, A. Brew, M. Jones, W. Evans, Coombs, Sowden-Taylor, Lydiate, Morgan, Sidoli, Castle, Burns, Price
Replacements: L. Evans for Coombs (73), A. Jones for Sidoli (73), Hall for Castle (58), Gustafson for Price (66)