Mike Le Bourgeois kicked Jersey into a 9-0 lead after 18 minutes. Leinster out-half Noel Reid exchanged penalties with his opposite number, before pulling one back before half-time to make it 12-6.
Colin McEntee's side got on top after the break, with Jordan Coghlan to the fore. Leo Auva'a muscled his way to a try, before captain Rhys Ruddock powered over in the corner.
Jersey pushed hard to try and steal the victory in a tense finish, but Leinster survived.