The former Manchester United captain was named by Walter Mazzarri as part of a strong Inter side, playing in a back three at the Stadio La Pineta in Pinzolo.
Vidic will face much tougher tests over the coming weeks in Inter's close-season preparations but played the first half before substitute Ibrahima Mbaye scored the only goal of the game in the second half.
The 19-year-old, who spent last season on loan at Livorno, headed home from a corner to make it two friendly wins from two for Inter.
Mazzarri's side got their close-season campaign up and running with a 6-1 victory over Trentino last week but were made to work much harder by Prato.
Mauro Icardi had the first opportunity - slicing a shot wide of goal with 11 minutes gone - before Mateo Kovacic dragged an effort off target following a surging run.
Prato, while stoic at the back, struggled to muster opportunities as they went in level at the break.
Vidic, Zdravko Kuzmanovic and Samir Handanovic made way for Marco Andreolli, Yann M'Vila and Juan Pablo Carrizo at half-time with Mazzarri making further changes throughout the second half.
The crucial one, however, was Mbaye's - the young defender nodding the winner within 60 seconds of his introduction.
Recently appointed captain Andrea Ranocchia was next to be taken off as Mazzarri's men looked to gear up for the International Champions Cup where they will meet Real Madrid, Manchester United and Roma.
