The Scots, with just one victory in the tournament since 2021, went ahead with Billy Allen scoring from a maul.
Federico Zanandrea profited from an interception to put Italy 7-5 ahead at the interval.
Niccolo Beni and Eduardo Todaro stretched Italy's lead before replacement Ollie Duncan's try gave hopes of a Scotland fightback, but the visitors knocked over a penalty in the closing moments secure the win.