Ezequiel Ponce scored for the Giallorossi Under-19s two minutes into the second half to cancel out Grigoris Kastanos' first-half spot kick as regular time finished 1-1.
There were no goals in extra time so a 12-yard showdown was needed to separate the sides.
Roma U19s' keeper Lorenzo Crisanto saved Guido Vadala's effort to hand Roma the advantage but Riccardo Marchizza's miss sent the shootout to sudden death.
Crisanto then thwarted Andrea Favilli and Lorenzo Grossi held his nerve to fire home the decisive spot kick.
Here's our gallery of Alberto De Rossi's boys celebrating their title triumph.
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