Treviso took control of the match when the Scarlets were a man down after Rhys Thomas was sinbinned.
Ludovico Nitoglia claimed a try and Kris Burton landed a penalty.
Welsh under-20 wing Liam Williams dragged the Scarlets back into the game with a try and Dan Newton added the conversion.
But a try from Australian winger Brendan Williams clinched victory for the Italians.
Burton finished up with 10 points, converting both tries and bagging a second penalty.
The Scarlets made six changes to their starting line-up with Aled Thomas taking over fly-half duties and Newton switching to full-back.
Williams was handed another start on the wing and Richie Pugh came into the back row for the injured Josh Turnbull.
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The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
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