Nigel Davies’ men always looked in control in Northern Italy and outscored their hosts by four tries to two.
Treviso fly-half Willem De Waal opened the scoring after just two minutes but Priestland soon nudged the visitors in front with two well-struck penalties.
Just before the half hour mark Dominic Day crashed over for the opening try. Josh Turnbull powered his way close before Day scooped up the ball and dived over, Priestland had no problems with the conversion.
The Scarlets half-back was soon lining up his second conversion attempt of the day after Dan Newton crossed for the visitors. A strong run from Morgan Stoddard created the space for the supporting Newton to score his first Heineken Cup try.
Treviso’s powerful pack hauled them back into the game, Robert Barbieri touching down following a 20 metre rolling drive. De Waal added the conversion for an 18-10 score line at the break.
Priestland drew first blood in the second half with his third penalty before Marco Filippucci scored the hosts second try.
The Flanker’s try gave the Italian’s hope but it was the Scarlets who stepped up with further tries from Gareth Maule and then Jonny Fa’amatuainu.
